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Talk:Dynamical system - Wikipedia

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If you would like to participate, please visit the project page, where you can join <a href="/wiki/Wikipedia_talk:WikiProject_Physics" title="Wikipedia talk:WikiProject Physics">the discussion</a> and see a list of open tasks.<span class="metadata wpb-metadata"><span class="wpb-project">Physics</span><span class="wpb-project_link">Wikipedia:WikiProject Physics</span><span class="wpb-banner_name">Template:WikiProject Physics</span><span class="wpb-assessment_cat">physics articles</span></span></td><td class="mbox-empty-cell"></td></tr><tr><td class="assess import-mid"><a href="/wiki/Category:Mid-importance_physics_articles" title="Category:Mid-importance physics articles">Mid</a></td><td class="mbox-text" colspan="2">This article has been rated as <b>Mid-importance</b> on the <a href="/wiki/Wikipedia:WikiProject_Physics/Quality_Control#Importance_scale" title="Wikipedia:WikiProject Physics/Quality Control">project's importance 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title="Wikipedia:WikiProject Systems">WikiProject Systems</a></b>, which collaborates on articles related to <a href="/wiki/System" title="System">systems</a> and <a href="/wiki/Systems_science" title="Systems science">systems science</a>.<span class="metadata wpb-metadata"><span class="wpb-project">Systems</span><span class="wpb-project_link">Wikipedia:WikiProject Systems</span><span class="wpb-banner_name">Template:WikiProject Systems</span><span class="wpb-assessment_cat">Systems articles</span></span></td><td class="mbox-empty-cell"></td></tr><tr><td class="assess import-top"><a href="/wiki/Category:Top-importance_Systems_articles" title="Category:Top-importance Systems articles">Top</a></td><td class="mbox-text" colspan="2">This article has been rated as <b>Top-importance</b> on the <a href="/wiki/Wikipedia:WikiProject_Systems/Assessment#Importance_scale" title="Wikipedia:WikiProject Systems/Assessment">project's importance scale</a>.</td></tr><tr><td><figure class="mw-default-size mw-halign-center" typeof="mw:File"><a href="/wiki/File:AsymptoticStabilityImpulseScilab.png" class="mw-file-description"><img alt="Taskforce icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/AsymptoticStabilityImpulseScilab.png/50px-AsymptoticStabilityImpulseScilab.png" decoding="async" width="50" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/AsymptoticStabilityImpulseScilab.png/75px-AsymptoticStabilityImpulseScilab.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/AsymptoticStabilityImpulseScilab.png/99px-AsymptoticStabilityImpulseScilab.png 2x" data-file-width="530" data-file-height="270"/></a><figcaption></figcaption></figure></td><td class="mbox-text" colspan="2">This article is within the field of <a href="/wiki/Category:Systems_articles_in_dynamical_systems" title="Category:Systems articles in dynamical systems">Dynamical systems</a>.</td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237879475"><table class="box-backwards-copy plainlinks tmbox tmbox-notice" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/File:Newspaper_Cover.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Newspaper_Cover.svg/50px-Newspaper_Cover.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/11/Newspaper_Cover.svg/75px-Newspaper_Cover.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/11/Newspaper_Cover.svg/100px-Newspaper_Cover.svg.png 2x" data-file-width="120" data-file-height="120"/></a></span></td><td class="mbox-text">This article is substantially duplicated by a piece in an external publication. Since the external publication copied Wikipedia rather than the reverse, please do not flag this article as a copyright violation of the following source: <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation cs2">Vandome, A. F., Miller, F. P., &amp; McBrewster, J. (2009), <i>Dynamical system</i>, Alphascript Publishing</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=Dynamical+system&amp;rft.pub=Alphascript+Publishing&amp;rft.date=2009&amp;rft.au=Vandome%2C+A.+F.%2C+Miller%2C+F.+P.%2C+%26+McBrewster%2C+J.&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3ATalk%3ADynamical+system" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Citation" title="Template:Citation">citation</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></li></ul> <table class="mw-collapsible mw-collapsed" style="width:100%; background-color: #f8eaba;"><tbody><tr><th>Additional comments</th></tr><tr><td style="background-color: white; border: 1px solid #c0c090; padding: 0.25em 0.5em;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/690728079">690728079</a>, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9786130081171" title="Special:BookSources/9786130081171">9786130081171</a>.</td></tr></tbody></table></td></tr></tbody></table> <p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237879475"> </p> <table id="archivebox" role="presentation" class="tmbox tmbox-notice mbox-small" style="text-align: center; padding: 1em;"> <tbody><tr> <td style="padding:0.6em 0 0.25em;"> <div style="width:100%; overflow:hidden;"><span typeof="mw:File"><a href="/wiki/File:Replacement_filing_cabinet.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/2/2a/Replacement_filing_cabinet.svg/40px-Replacement_filing_cabinet.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/2/2a/Replacement_filing_cabinet.svg/60px-Replacement_filing_cabinet.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/2/2a/Replacement_filing_cabinet.svg/80px-Replacement_filing_cabinet.svg.png 2x" data-file-width="200" data-file-height="200"/></a></span><br/><b>Archives</b></div> </td></tr><tr> <td class="plainlinks"> <p><a href="/wiki/Talk:Dynamical_system/Archive_1" title="Talk:Dynamical system/Archive 1">1</a> </p> </td> </tr><tr><td style="padding-bottom:11px"><div class="mw-inputbox-centered" style=""><form name="searchbox" class="searchbox mw-inputbox-form" action="/wiki/Special:Search"><div class="cdx-text-input"><input class="mw-inputbox-input mw-searchInput searchboxInput cdx-text-input__input" name="search" placeholder="" size="22" dir="ltr"/></div><input type="hidden" value="Talk:Dynamical system/" name="prefix"/><br/><input type="submit" name="fulltext" value="Search archives" class="cdx-button"/><input type="hidden" value="Search" name="fulltext"/></form></div> </td></tr><tr><td style="padding:0px 10px; font-size:11.9px;"> <hr/> This page has archives. Sections older than <b>365 days</b> may be automatically archived by <span class="nowraplinks"><a href="/wiki/User:Lowercase_sigmabot_III" title="User:Lowercase sigmabot III">Lowercase sigmabot III</a></span> when more than 5 sections are present.</td></tr> </tbody></table> <meta property="mw:PageProp/toc"/> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><!--__DTSUBSCRIBEBUTTONDESKTOP__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-Dmharvey-2005-07-05T19:43:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-discrete_dynamical_systems?-2005-07-05T19:43:00.000Z&quot;,&quot;replies&quot;:[&quot;c-Dmharvey-2005-07-05T19:43:00.000Z-discrete_dynamical_systems?&quot;],&quot;text&quot;:&quot;discrete dynamical systems?&quot;,&quot;linkableTitle&quot;:&quot;discrete dynamical systems?&quot;}--><h2 id="discrete_dynamical_systems?" data-mw-thread-id="h-discrete_dynamical_systems?-2005-07-05T19:43:00.000Z"><span id="discrete_dynamical_systems.3F"></span><span data-mw-comment-start="" id="h-discrete_dynamical_systems?-2005-07-05T19:43:00.000Z"></span>discrete dynamical systems?<span data-mw-comment-end="h-discrete_dynamical_systems?-2005-07-05T19:43:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Dynamical_system&amp;action=edit&amp;section=1" title="Edit section: discrete dynamical systems?"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><!--__DTELLIPSISBUTTON__{"threadItem":{"headingLevel":2,"name":"h-Dmharvey-2005-07-05T19:43:00.000Z","type":"heading","level":0,"id":"h-discrete_dynamical_systems?-2005-07-05T19:43:00.000Z","replies":["c-Dmharvey-2005-07-05T19:43:00.000Z-discrete_dynamical_systems?"]}}--><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"><!--__DTLATESTCOMMENTTHREAD__{"id":"c-Dmharvey-2005-07-05T19:43:00.000Z-discrete_dynamical_systems?","timestamp":"2005-07-05T19:43:00.000Z"}__--><!--__DTCOMMENTCOUNT__1__--><!--__DTAUTHORCOUNT__1__--></div><div class="ext-discussiontools-init-section-actions"><!--__DTSUBSCRIBEBUTTONMOBILE__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-Dmharvey-2005-07-05T19:43:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-discrete_dynamical_systems?-2005-07-05T19:43:00.000Z&quot;,&quot;replies&quot;:[&quot;c-Dmharvey-2005-07-05T19:43:00.000Z-discrete_dynamical_systems?&quot;],&quot;text&quot;:&quot;discrete dynamical systems?&quot;,&quot;linkableTitle&quot;:&quot;discrete dynamical systems?&quot;}--></div></div></div> <p><span data-mw-comment-start="" id="c-Dmharvey-2005-07-05T19:43:00.000Z-discrete_dynamical_systems?"></span>The term <a href="/wiki/Discrete_dynamical_system" class="mw-redirect" title="Discrete dynamical system">discrete dynamical system</a> redirects here, but there is (almost) no discussion of the topic here. Would be nice for somebody to write it. <a href="/wiki/User:Dmharvey" title="User:Dmharvey">Dmharvey</a> <a href="/wiki/User_talk:Dmharvey" title="User talk:Dmharvey">Talk</a> <a href="https://en.wikipedia.org/wiki/Talk:Dynamical_system#c-Dmharvey-2005-07-05T19:43:00.000Z-discrete_dynamical_systems?" class="ext-discussiontools-init-timestamplink">19:43, 5 July 2005 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Dmharvey-2005-07-05T19:43:00.000Z-discrete_dynamical_systems?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span><!--__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2005-07-05T19:43:00.000Z","author":"Dmharvey","type":"comment","level":1,"id":"c-Dmharvey-2005-07-05T19:43:00.000Z-discrete_dynamical_systems?","replies":[]}}--></span><span data-mw-comment-end="c-Dmharvey-2005-07-05T19:43:00.000Z-discrete_dynamical_systems?"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><!--__DTSUBSCRIBEBUTTONDESKTOP__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-XaosBits-2015-12-29T05:53:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-Definition,_again-2015-12-29T05:53:00.000Z&quot;,&quot;replies&quot;:[&quot;c-XaosBits-2015-12-29T05:53:00.000Z-Definition,_again&quot;],&quot;text&quot;:&quot;Definition, again&quot;,&quot;linkableTitle&quot;:&quot;Definition, again&quot;}--><h2 id="Definition,_again" data-mw-thread-id="h-Definition,_again-2015-12-29T05:53:00.000Z"><span id="Definition.2C_again"></span><span data-mw-comment-start="" id="h-Definition,_again-2015-12-29T05:53:00.000Z"></span>Definition, again<span data-mw-comment-end="h-Definition,_again-2015-12-29T05:53:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Dynamical_system&amp;action=edit&amp;section=2" title="Edit section: Definition, again"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><!--__DTELLIPSISBUTTON__{"threadItem":{"headingLevel":2,"name":"h-XaosBits-2015-12-29T05:53:00.000Z","type":"heading","level":0,"id":"h-Definition,_again-2015-12-29T05:53:00.000Z","replies":["c-XaosBits-2015-12-29T05:53:00.000Z-Definition,_again"]}}--><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"><!--__DTLATESTCOMMENTTHREAD__{"id":"c-XaosBits-2015-12-29T05:53:00.000Z-Definition,_again","timestamp":"2015-12-29T05:53:00.000Z"}__--><!--__DTCOMMENTCOUNT__1__--><!--__DTAUTHORCOUNT__1__--></div><div class="ext-discussiontools-init-section-actions"><!--__DTSUBSCRIBEBUTTONMOBILE__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-XaosBits-2015-12-29T05:53:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-Definition,_again-2015-12-29T05:53:00.000Z&quot;,&quot;replies&quot;:[&quot;c-XaosBits-2015-12-29T05:53:00.000Z-Definition,_again&quot;],&quot;text&quot;:&quot;Definition, again&quot;,&quot;linkableTitle&quot;:&quot;Definition, again&quot;}--></div></div></div> <p><span data-mw-comment-start="" id="c-XaosBits-2015-12-29T05:53:00.000Z-Definition,_again"></span>I changed the definition back. A dynamical system is a smooth function from a manifold to itself dependent on one parameter, time. While the manifold could be replaced by a more general set, loosing smoothness takes one to ergodic theory or symbolic dynamics. The parameter needs to be a monoid traditionally written in additive form. One could just formalize that definition, but the challenge is to re-write it so that someone with high school mathematics can follow the definition. </p><p>From what I replaced, I liked the use of <i>relationship</i> instead of function and <i>responding to their own values</i>, which emphasizes the mapping a point of the manifold back onto itself. But I could not get it to work. Maybe someone else could try. <a href="/wiki/User:XaosBits" title="User:XaosBits">XaosBits</a> (<a href="/wiki/User_talk:XaosBits" title="User talk:XaosBits">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Dynamical_system#c-XaosBits-2015-12-29T05:53:00.000Z-Definition,_again" class="ext-discussiontools-init-timestamplink">05:53, 29 December 2015 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-XaosBits-2015-12-29T05:53:00.000Z-Definition,_again"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span><!--__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2015-12-29T05:53:00.000Z","author":"XaosBits","type":"comment","level":1,"id":"c-XaosBits-2015-12-29T05:53:00.000Z-Definition,_again","replies":[]}}--></span><span data-mw-comment-end="c-XaosBits-2015-12-29T05:53:00.000Z-Definition,_again"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><!--__DTSUBSCRIBEBUTTONDESKTOP__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-InternetArchiveBot-2016-09-11T19:42:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-External_links_modified-2016-09-11T19:42:00.000Z&quot;,&quot;replies&quot;:[&quot;c-InternetArchiveBot-2016-09-11T19:42:00.000Z-External_links_modified&quot;],&quot;text&quot;:&quot;External links modified&quot;,&quot;linkableTitle&quot;:&quot;External links modified&quot;}--><h2 id="External_links_modified" data-mw-thread-id="h-External_links_modified-2016-09-11T19:42:00.000Z"><span data-mw-comment-start="" id="h-External_links_modified-2016-09-11T19:42:00.000Z"></span>External links modified<span data-mw-comment-end="h-External_links_modified-2016-09-11T19:42:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Dynamical_system&amp;action=edit&amp;section=3" title="Edit section: External links modified"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><!--__DTELLIPSISBUTTON__{"threadItem":{"headingLevel":2,"name":"h-InternetArchiveBot-2016-09-11T19:42:00.000Z","type":"heading","level":0,"id":"h-External_links_modified-2016-09-11T19:42:00.000Z","replies":["c-InternetArchiveBot-2016-09-11T19:42:00.000Z-External_links_modified"]}}--><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"><!--__DTLATESTCOMMENTTHREAD__{"id":"c-InternetArchiveBot-2016-09-11T19:42:00.000Z-External_links_modified","timestamp":"2016-09-11T19:42:00.000Z"}__--><!--__DTCOMMENTCOUNT__1__--><!--__DTAUTHORCOUNT__1__--></div><div class="ext-discussiontools-init-section-actions"><!--__DTSUBSCRIBEBUTTONMOBILE__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-InternetArchiveBot-2016-09-11T19:42:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-External_links_modified-2016-09-11T19:42:00.000Z&quot;,&quot;replies&quot;:[&quot;c-InternetArchiveBot-2016-09-11T19:42:00.000Z-External_links_modified&quot;],&quot;text&quot;:&quot;External links modified&quot;,&quot;linkableTitle&quot;:&quot;External links modified&quot;}--></div></div></div> <p><span data-mw-comment-start="" id="c-InternetArchiveBot-2016-09-11T19:42:00.000Z-External_links_modified"></span>Hello fellow Wikipedians, </p><p>I have just modified 3 external links on <a href="/wiki/Dynamical_system" title="Dynamical system">Dynamical system</a>. 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href="https://en.wikipedia.org/wiki/Talk:Dynamical_system#c-InternetArchiveBot-2016-09-11T19:42:00.000Z-External_links_modified" class="ext-discussiontools-init-timestamplink">19:42, 11 September 2016 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-InternetArchiveBot-2016-09-11T19:42:00.000Z-External_links_modified"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span><!--__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2016-09-11T19:42:00.000Z","author":"InternetArchiveBot","type":"comment","level":1,"id":"c-InternetArchiveBot-2016-09-11T19:42:00.000Z-External_links_modified","replies":[]}}--></span><span data-mw-comment-end="c-InternetArchiveBot-2016-09-11T19:42:00.000Z-External_links_modified"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><!--__DTSUBSCRIBEBUTTONDESKTOP__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-Fgnievinski-2021-07-15T21:03:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system-2021-07-15T21:03:00.000Z&quot;,&quot;replies&quot;:[&quot;c-MarkH21-2021-09-16T08:31:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system&quot;,&quot;c-Fgnievinski-2021-07-15T21:03:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system&quot;],&quot;text&quot;:&quot;Proposed merge of Dynamical system (definition) into Dynamical system&quot;,&quot;linkableTitle&quot;:&quot;Proposed merge of Dynamical system (definition) into Dynamical system&quot;}--><h2 id="Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system" data-mw-thread-id="h-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system-2021-07-15T21:03:00.000Z"><span id="Proposed_merge_of_Dynamical_system_.28definition.29_into_Dynamical_system"></span><span data-mw-comment-start="" id="h-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system-2021-07-15T21:03:00.000Z"></span>Proposed merge of <a href="/wiki/Dynamical_system_(definition)" class="mw-redirect" title="Dynamical system (definition)">Dynamical system (definition)</a> into <a href="/wiki/Dynamical_system" title="Dynamical system">Dynamical system</a><span data-mw-comment-end="h-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system-2021-07-15T21:03:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Dynamical_system&amp;action=edit&amp;section=4" title="Edit section: Proposed merge of Dynamical system (definition) into Dynamical system"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><!--__DTELLIPSISBUTTON__{"threadItem":{"headingLevel":2,"name":"h-Fgnievinski-2021-07-15T21:03:00.000Z","type":"heading","level":0,"id":"h-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system-2021-07-15T21:03:00.000Z","replies":["c-MarkH21-2021-09-16T08:31:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system","c-Fgnievinski-2021-07-15T21:03:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system"]}}--><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"><!--__DTLATESTCOMMENTTHREAD__{"id":"c-MarkH21-2021-09-16T08:31:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system","timestamp":"2021-09-16T08:31:00.000Z"}__--><!--__DTCOMMENTCOUNT__2__--><!--__DTAUTHORCOUNT__2__--></div><div class="ext-discussiontools-init-section-actions"><!--__DTSUBSCRIBEBUTTONMOBILE__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-Fgnievinski-2021-07-15T21:03:00.000Z&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system-2021-07-15T21:03:00.000Z&quot;,&quot;replies&quot;:[&quot;c-MarkH21-2021-09-16T08:31:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system&quot;,&quot;c-Fgnievinski-2021-07-15T21:03:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system&quot;],&quot;text&quot;:&quot;Proposed merge of Dynamical system (definition) into Dynamical system&quot;,&quot;linkableTitle&quot;:&quot;Proposed merge of Dynamical system (definition) into Dynamical system&quot;}--></div></div></div> <div class="boilerplate discussion-archived mw-archivedtalk" style="background-color: var(--background-color-progressive-subtle, #f5f3ef); color: var(--color-base, inherit); overflow:auto; margin: 1em 0 0 0; padding: 0 10px 0 10px; border: 1px solid var(--border-color-subtle, #aaa)"> <div class="boilerplate-header"> <dl><dd><i><span data-mw-comment-start="" id="c-MarkH21-2021-09-16T08:31:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system"></span>The following discussion is closed. <span style="color:var(--color-error, red)"><b>Please do not modify it.</b></span> Subsequent comments should be made in a new section.</i> <i>A summary of the conclusions reached follows.</i> <dl><dd>The result of this discussion was <b>Merge</b>. — <span style="font-family:Trebuchet MS;font-size:100%;color:black;background-color:transparent;;"><a href="/wiki/User:MarkH21" title="User:MarkH21">MarkH<sub><small>21</small></sub></a><sup><a href="/wiki/User_talk:MarkH21" title="User talk:MarkH21"><span style="background-color:navy; color:white;">talk</span></a></sup></span> <a href="https://en.wikipedia.org/wiki/Talk:Dynamical_system#c-MarkH21-2021-09-16T08:31:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system" class="ext-discussiontools-init-timestamplink">08:31, 16 September 2021 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-MarkH21-2021-09-16T08:31:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span><!--__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2021-09-16T08:31:00.000Z","author":"MarkH21","type":"comment","level":2,"id":"c-MarkH21-2021-09-16T08:31:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system","replies":[]}}--></span><span data-mw-comment-end="c-MarkH21-2021-09-16T08:31:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system"></span></dd></dl></dd></dl> <hr/> </div> <p><span data-mw-comment-start="" id="c-Fgnievinski-2021-07-15T21:03:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system"></span>"definition" is the main aspect of any topic <a href="/wiki/User:Fgnievinski" class="mw-redirect" title="User:Fgnievinski">fgnievinski</a> (<a href="/wiki/User_talk:Fgnievinski" title="User talk:Fgnievinski">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Dynamical_system#c-Fgnievinski-2021-07-15T21:03:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system" class="ext-discussiontools-init-timestamplink">21:03, 15 July 2021 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Fgnievinski-2021-07-15T21:03:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span><!--__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"2021-07-15T21:03:00.000Z","author":"Fgnievinski","type":"comment","level":1,"id":"c-Fgnievinski-2021-07-15T21:03:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system","replies":[]}}--></span><span data-mw-comment-end="c-Fgnievinski-2021-07-15T21:03:00.000Z-Proposed_merge_of_Dynamical_system_(definition)_into_Dynamical_system"></span> </p> <div style="padding-left: 1.6em; font-style: italic; border-top: 1px solid #a2a9b1; margin: 0.5em 0; padding-top: 0.5em">The discussion above is closed. <b style="color: var(--color-error, red);">Please do not modify it.</b> Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.</div> </div><div style="clear:both;" class=""></div> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><!--__DTSUBSCRIBEBUTTONDESKTOP__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-RowanElder-20240929134700&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-\&quot;Ergodic_systems\&quot;_section_organization-20240929134700&quot;,&quot;replies&quot;:[&quot;c-RowanElder-20240929134700-\&quot;Ergodic_systems\&quot;_section_organization&quot;],&quot;text&quot;:&quot;\&quot;Ergodic systems\&quot; section organization&quot;,&quot;linkableTitle&quot;:&quot;\&quot;Ergodic systems\&quot; section organization&quot;}--><h2 id="&quot;Ergodic_systems&quot;_section_organization" data-mw-thread-id="h-&quot;Ergodic_systems&quot;_section_organization-20240929134700"><span id=".22Ergodic_systems.22_section_organization"></span><span data-mw-comment-start="" id="h-&quot;Ergodic_systems&quot;_section_organization-20240929134700"></span>"Ergodic systems" section organization<span data-mw-comment-end="h-&quot;Ergodic_systems&quot;_section_organization-20240929134700"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Dynamical_system&amp;action=edit&amp;section=5" title="Edit section: &quot;Ergodic systems&quot; section organization"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><!--__DTELLIPSISBUTTON__{"threadItem":{"headingLevel":2,"name":"h-RowanElder-20240929134700","type":"heading","level":0,"id":"h-\"Ergodic_systems\"_section_organization-20240929134700","replies":["c-RowanElder-20240929134700-\"Ergodic_systems\"_section_organization"]}}--><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"><!--__DTLATESTCOMMENTTHREAD__{"id":"c-RowanElder-20240929134700-\"Ergodic_systems\"_section_organization","timestamp":"20240929134700"}__--><!--__DTCOMMENTCOUNT__1__--><!--__DTAUTHORCOUNT__1__--></div><div class="ext-discussiontools-init-section-actions"><!--__DTSUBSCRIBEBUTTONMOBILE__{&quot;headingLevel&quot;:2,&quot;name&quot;:&quot;h-RowanElder-20240929134700&quot;,&quot;type&quot;:&quot;heading&quot;,&quot;level&quot;:0,&quot;id&quot;:&quot;h-\&quot;Ergodic_systems\&quot;_section_organization-20240929134700&quot;,&quot;replies&quot;:[&quot;c-RowanElder-20240929134700-\&quot;Ergodic_systems\&quot;_section_organization&quot;],&quot;text&quot;:&quot;\&quot;Ergodic systems\&quot; section organization&quot;,&quot;linkableTitle&quot;:&quot;\&quot;Ergodic systems\&quot; section organization&quot;}--></div></div></div> <p><span data-mw-comment-start="" id="c-RowanElder-20240929134700-&quot;Ergodic_systems&quot;_section_organization"></span>Finite time solutions are an extreme opposite of ergodic behavior. Nonlinear and chaotic systems are not a subclass of ergodic systems. Finite time solutions do require nonlinearity. The organization here therefore makes very little sense. <a href="/wiki/User:RowanElder" title="User:RowanElder">RowanElder</a> (<a href="/wiki/User_talk:RowanElder" title="User talk:RowanElder">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Dynamical_system#c-RowanElder-20240929134700-&quot;Ergodic_systems&quot;_section_organization" class="ext-discussiontools-init-timestamplink">13:47, 29 September 2024 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-RowanElder-20240929134700-&quot;Ergodic_systems&quot;_section_organization"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span><!--__DTELLIPSISBUTTON__{"threadItem":{"timestamp":"20240929134700","author":"RowanElder","type":"comment","level":1,"id":"c-RowanElder-20240929134700-\"Ergodic_systems\"_section_organization","replies":[]}}--></span><span data-mw-comment-end="c-RowanElder-20240929134700-&quot;Ergodic_systems&quot;_section_organization"></span> </p> <!-- NewPP limit report Parsed by mw‐web.eqiad.main‐5dc468848‐4wgjr Cached time: 20241123182408 Cache expiry: 864000 Reduced expiry: true Complications: [vary‐revision‐sha1, vary‐revision‐id, show‐toc] DiscussionTools time usage: 0.024 seconds CPU time usage: 0.379 seconds Real time usage: 0.647 seconds Preprocessor visited node count: 1568/1000000 Post‐expand include size: 43606/2097152 bytes Template argument size: 1473/2097152 bytes Highest expansion depth: 16/100 Expensive parser function count: 24/500 Unstrip recursion depth: 0/20 Unstrip post‐expand size: 34755/5000000 bytes Lua time usage: 0.237/10.000 seconds Lua memory usage: 6062979/52428800 bytes Number of Wikibase entities loaded: 0/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 555.221 1 -total 41.60% 230.995 1 Template:WikiProject_banner_shell 40.36% 224.108 1 Template:Backwardscopy 15.01% 83.362 1 Template:WikiProject_Mathematics 11.91% 66.108 1 Template:Archive_box 6.72% 37.318 1 Template:WikiProject_Physics 6.10% 33.895 11 Template:Th/abp 4.76% 26.419 1 Template:Check_talk_wp 4.35% 24.170 1 Template:Category_handler 2.85% 15.811 1 Template:WikiProject_Systems --> <!-- Saved in parser cache with key enwiki:pcache:idhash:9089-0!canonical and timestamp 20241123182408 and revision id 1248592425. 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