Document Zbl 1531.14024

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Math., New Ser.</a> <a href="/?q=in%3A499415" title="Articles in this Issue">29, No. 4, Paper No. 65, 41 p. (2023)</a>. </div> <div class="abstract">Summary: In topological dynamics, the Gromov-Yomdin theorem states that the topological entropy of a holomorphic automorphism $f$ of a smooth projective variety is equal to the logarithm of the spectral radius of the induced map $f^\ast$. In order to establish a categorical analogue of the Gromov-Yomdin theorem, one first needs to find a categorical analogue of a holomorphic automorphism. In this paper, we propose a categorical analogue of a holomorphic automorphism and prove that the Gromov-Yomdin type theorem holds for them.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A14F08" title="MSC2020">14F08</a> </td> <td class="space"> Derived categories of sheaves, dg categories, and related constructions in algebraic geometry </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A18G80" title="MSC2020">18G80</a> </td> <td class="space"> Derived categories, triangulated categories </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A37B40" title="MSC2020">37B40</a> </td> <td class="space"> Topological entropy </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A53D37" title="MSC2020">53D37</a> </td> <td class="space"> Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category </td> </tr></table> </div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1531.14024" data-ciurl="/ci/07733766" data-biburl="/bibtex/07733766.bib" data-amsurl="/amsrefs/07733766.bib" data-xmlurl="/xml/07733766.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07733766.pdf" title="Zbl 1531.14024 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s00029-023-00870-x" aria-label="DOI for “On Gromov-Yomdin type theorems and a categorical interpretation of holomorphicity”" title="10.1007/s00029-023-00870-x">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2110.12597"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Barbacovi, F., Kim, J.: Entropy of the composition of two spherical twists. 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