{"id":1616,"date":"2025-09-09T09:33:55","date_gmt":"2025-09-09T09:33:55","guid":{"rendered":"https:\/\/www2.isep.ipp.pt\/coupled80\/?page_id=1616"},"modified":"2025-09-09T09:35:32","modified_gmt":"2025-09-09T09:35:32","slug":"john-guckenheimer","status":"publish","type":"page","link":"https:\/\/www2.isep.ipp.pt\/coupled80\/?page_id=1616","title":{"rendered":"John Guckenheimer"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"287\" height=\"425\" src=\"https:\/\/www2.isep.ipp.pt\/coupled80\/wp-content\/uploads\/2024\/12\/photo_crop.jpg\" alt=\"\" class=\"wp-image-1324\" srcset=\"https:\/\/www2.isep.ipp.pt\/coupled80\/wp-content\/uploads\/2024\/12\/photo_crop.jpg 287w, https:\/\/www2.isep.ipp.pt\/coupled80\/wp-content\/uploads\/2024\/12\/photo_crop-203x300.jpg 203w\" sizes=\"auto, (max-width: 287px) 100vw, 287px\" \/><figcaption class=\"wp-element-caption\">Cornell University, USA<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Title:<\/strong> The Legacy of Cartwright and Littlewood<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Abstract:<\/strong> This talk is based on my contribution to a centennial volume of the Journal of the London Mathematical Society describing mathematical developments spawned by selected papers.<br>Mary Cartwright and John E. Littlewood published a seminal paper on the forced van der Pol equation in 1945, the birth year of &#8220;Coupled 80&#8221;.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Their paper describes work begun in response to a request by the British Radio Research Board for mathematicians to help during World War II. It presents a &#8220;preliminary survey&#8221; of the first mathematical analysis of chaos in a non-conservative dynamical system of differential equations. They inspired further work on dynamical systems, including Smale&#8217;s famous horseshoe example. The details of their work appeared only in 1957 in a paper whose complexity is infamous. I recount the history of this work along with my contributions with collaborators to extend it, recasting the results to be much more accessible.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><a href=\"https:\/\/www2.isep.ipp.pt\/coupled80\/?page_id=27\">&lt;&lt; BACK<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Title: The Legacy of Cartwright and Littlewood Abstract: This talk is based on my contribution to a centennial volume of the Journal of the London Mathematical Society describing mathematical developments spawned by selected papers.Mary Cartwright and John E. Littlewood published a seminal paper on the forced van der Pol equation in 1945, the birth year &hellip; <\/p>\n","protected":false},"author":2,"featured_media":0,"parent":1090,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1616","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/pages\/1616","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=1616"}],"version-history":[{"count":1,"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/pages\/1616\/revisions"}],"predecessor-version":[{"id":1618,"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/pages\/1616\/revisions\/1618"}],"up":[{"embeddable":true,"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=\/wp\/v2\/pages\/1090"}],"wp:attachment":[{"href":"https:\/\/www2.isep.ipp.pt\/coupled80\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1616"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}