{"id":682,"date":"2022-04-04T20:35:44","date_gmt":"2022-04-04T20:35:44","guid":{"rendered":"https:\/\/pages.charlotte.edu\/colloquium\/?p=682"},"modified":"2022-04-18T16:31:41","modified_gmt":"2022-04-18T16:31:41","slug":"friday-april-8-2022-1100-1200-via-zoom%ef%bf%bc","status":"publish","type":"post","link":"https:\/\/pages.charlotte.edu\/colloquium\/blog\/2022\/04\/04\/friday-april-8-2022-1100-1200-via-zoom%ef%bf%bc\/","title":{"rendered":"Friday, April 8, 2022, 11:00-12:00, via Zoom"},"content":{"rendered":"\n<p><strong>Speaker:<\/strong>&nbsp;Dr. <a href=\"https:\/\/www.baylor.edu\/math\/index.php?id=89972\">Jonathan Meddaugh<\/a> from Baylor University (invited by Will Brian)<\/p>\n\n\n\n<p><strong>Title:<\/strong>&nbsp;Shadowing in Dynamical Systems: When are approximate orbits meaningful?<\/p>\n\n\n\n<p><strong>Abstract:<\/strong>&nbsp;&nbsp;In a discrete dynamical system f: X <strong>\u2192<\/strong> X, the orbit of a point x \u03f5 X is the sequence x, f(x), f\u00b2(x), . . . . In even modestly complex systems, small errors compound rapidly in computations of orbits, leading to true orbits and computed orbits that are wildly different. Surprisingly, however, there is a large class of systems for which these approximate orbits can yield useful qualitative information about the dynamics of the system\u2014systems with shadowing. Informally, a dynamical system f: X <strong>\u2192<\/strong> X has the shadowing property provided that for any specified level of tolerance, there is a level of precision that guarantees that any approximate orbit which is computed with this level of precision is itself approximated (shadowed) within the specified tolerance by a true orbit for the system. In this talk, we will discuss the shadowing property with a focus on recent results concerning characterizations of this property and its relative prevalence in certain classes of dynamical systems.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Speaker:&nbsp;Dr. Jonathan Meddaugh from Baylor University (invited by Will Brian) Title:&nbsp;Shadowing in Dynamical Systems: When are approximate orbits meaningful? Abstract:&nbsp;&nbsp;In a discrete dynamical system f: X \u2192 X, the orbit of a point x \u03f5 X is the sequence x, f(x), f\u00b2(x), . . . . In even modestly complex systems, small errors compound rapidly [&hellip;]<\/p>\n","protected":false},"author":2373,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[],"class_list":["post-682","post","type-post","status-publish","format-standard","hentry","category-spring-2022"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3kCtT-b0","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/682","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/users\/2373"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/comments?post=682"}],"version-history":[{"count":2,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/682\/revisions"}],"predecessor-version":[{"id":689,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/posts\/682\/revisions\/689"}],"wp:attachment":[{"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/media?parent=682"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/categories?post=682"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.charlotte.edu\/colloquium\/wp-json\/wp\/v2\/tags?post=682"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}