{"id":1335,"date":"2024-12-30T19:31:16","date_gmt":"2024-12-30T19:31:16","guid":{"rendered":"https:\/\/www2.isep.ipp.pt\/coupled80\/?page_id=1335"},"modified":"2024-12-30T19:44:11","modified_gmt":"2024-12-30T19:44:11","slug":"b-w-rink","status":"publish","type":"page","link":"https:\/\/www2.isep.ipp.pt\/coupled80\/?page_id=1335","title":{"rendered":"B.W. Rink"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"682\" height=\"1024\" src=\"https:\/\/www2.isep.ipp.pt\/coupled80\/wp-content\/uploads\/2024\/12\/Bob-Rink-3-1-682x1024.jpg\" alt=\"\" class=\"wp-image-1336\" style=\"width:160px;height:auto\" srcset=\"https:\/\/www2.isep.ipp.pt\/coupled80\/wp-content\/uploads\/2024\/12\/Bob-Rink-3-1-682x1024.jpg 682w, https:\/\/www2.isep.ipp.pt\/coupled80\/wp-content\/uploads\/2024\/12\/Bob-Rink-3-1-200x300.jpg 200w, https:\/\/www2.isep.ipp.pt\/coupled80\/wp-content\/uploads\/2024\/12\/Bob-Rink-3-1-768x1154.jpg 768w, https:\/\/www2.isep.ipp.pt\/coupled80\/wp-content\/uploads\/2024\/12\/Bob-Rink-3-1-1022x1536.jpg 1022w, https:\/\/www2.isep.ipp.pt\/coupled80\/wp-content\/uploads\/2024\/12\/Bob-Rink-3-1-1363x2048.jpg 1363w, https:\/\/www2.isep.ipp.pt\/coupled80\/wp-content\/uploads\/2024\/12\/Bob-Rink-3-1-scaled.jpg 1704w\" sizes=\"auto, (max-width: 682px) 100vw, 682px\" \/><figcaption class=\"wp-element-caption\">Vrije Universiteit Amsterdam<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Title:<\/strong> Non-Birkhoff periodic orbits in symmetric planar billiards \u00a0\u00a0\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Abstract:<\/strong> \u00a0A classical result of Poincar\u00e9 and Birkhoff implies that every smooth convex planar billiard admits at least two periodic orbits of any rational rotation number. These orbit are called\u00a0<em>Birkhoff orbits<\/em>\u00a0and they admit a simple geometric description: they have the shape of regular polygon. In this talk I will present results on the existence of non-Birkhoff periodic orbits in symmetric convex planar billiards. The main result is a quantitative criterion for the existence of such orbits with prescribed period, rotation number, and spatiotemporal symmetry. As a corollary we prove that arbitrarily small analytical perturbations of the circular billiard have non-Birkhoff orbits of any rational rotation number. This is joint work with Casper Oelen and Mattia Sensi.\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Bio:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Education:<br>2003: PhD in Mathematics, Utrecht University. Advisors: Ferdinand Verhulst and Hans Duistermaat<br>1999: MSc\/BSc in Mathematics, Utrecht University, cum laude<br>Faculty and postdoctoral positions:<br>2016 &#8211; &#8230; : Full professor, Vrije Universiteit Amsterdam<br>2014 &#8211; 2016: Associate professor, Vrije Universiteit Amsterdam<br>2007 &#8211; 2014: Assistant professor, Vrije Universiteit Amsterdam<br>2004 &#8211; 2007: Postdoc, <a href=\"https:\/\/www.imperial.ac.uk\/mathematics\/\" target=\"_blank\" rel=\"noreferrer noopener\">Imperial College London<\/a><\/li>\n\n\n\n<li>Grants and prizes<br>SMRI International visitor grant (8 kAUD), 2023<br>SMRI International visitor grant (12 kAUD), 2020<br>SIGEST outstanding paper award, awarded by SIAM for the article <a href=\"https:\/\/epubs.siam.org\/doi\/10.1137\/16M106861X\" target=\"_blank\" rel=\"noreferrer noopener\">Center manifolds of coupled cell networks<\/a> published in the SIAM J. Mathematical Analysis<br>NWO Vrije competitie grant &#8220;Variational methods for quasi-periodicity&#8221; (202 k\u20ac), 2009<br>NWO Veni grant &#8220;Hamiltonian lattice dynamical systems&#8221; (208 k\u20ac), 2007<br>MSRI Membership grant &#8220;Dynamical systems&#8221; (8 kUSD), 2007<br>EPSRC Postdoctoral fellowship grant &#8220;Geometry and near-integrability of Hamiltonian dynamical systems&#8221; (113 kGBP), 2004<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Title: Non-Birkhoff periodic orbits in symmetric planar billiards \u00a0\u00a0\u00a0 Abstract: \u00a0A classical result of Poincar\u00e9 and Birkhoff implies that every smooth convex planar billiard admits at least two periodic orbits of any rational rotation number. These orbit are called\u00a0Birkhoff orbits\u00a0and they admit a simple geometric description: they have the shape of regular polygon. In this &hellip; <\/p>\n","protected":false},"author":2,"featured_media":0,"parent":239,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1335","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/pages\/1335","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1335"}],"version-history":[{"count":5,"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/pages\/1335\/revisions"}],"predecessor-version":[{"id":1346,"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/pages\/1335\/revisions\/1346"}],"up":[{"embeddable":true,"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/pages\/239"}],"wp:attachment":[{"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1335"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}