{"649367":{"#nid":"649367","#data":{"type":"event","title":"PhD Defense by Adrian Perez Bustamante,","body":[{"value":"\u003Cp\u003ETitle:\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDomains of Analyticity and Gevrey estimates in weakly dissipative systems.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDate:\u003C\/p\u003E\r\n\r\n\u003Cp\u003EFriday, August 27, 2021.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003ETime:\u003C\/p\u003E\r\n\r\n\u003Cp\u003E12:00pm - 2:00pm\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003ELocation:\u003C\/p\u003E\r\n\r\n\u003Cp\u003EBluejeans meeting: \u003Ca href=\u0022https:\/\/bluejeans.com\/417759047\/0103\u0022\u003Ehttps:\/\/bluejeans.com\/417759047\/0103\u003C\/a\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003ECommitte members:\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Rafael de la Llave (Advisor) - School of Mathematics, Georgia Institute of Technology\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Chongchun Zeng - School of Mathematics, Georgia Institute of Technology\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Molei Tao - School of Mathematics, Georgia Institute of Technology\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Alex Blumenthal - School of Mathematics, Georgia Institute of Technology\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Alessandra Celletti - Department of Mathematics, University of Rome Tor Vergata\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003EAbstract:\u003C\/p\u003E\r\n\r\n\u003Cp\u003EWe consider the problem of following quasi-periodic tori in perturbations of Hamiltonian systems which involve friction and external forcing.\u003Cbr \/\u003E\r\nIn the first part, we study a family of dissipative standard maps of the cylinder for which the dissipation is a function of a small complex parameter of perturbation, $\\varepsilon$.\u0026nbsp; We compute perturbative expansions formally in $\\varepsilon$ and use them to estimate the shape of the domains of analyticity of invariant circles as functions of $\\varepsilon$. We also give evidence that the functions might belong to a Gevrey class. The numerical computations we perform support conjectures on the shape of the domains of analyticity.\u003C\/p\u003E\r\n\r\n\u003Cp\u003EIn the second part, we study rigorously the(divergent) series of formal expansions of the torus obtained using Lindstedt method.\u0026nbsp;\u0026nbsp; We show that, for some systems in the literature, the series is Gevrey. We hope that the method of proof can be of independent interest: We develop KAM estimates for the divergent series. In contrast with the regular KAM method, we loose control of all the domains, so that there is no convergence, but we can generate enough control to show that the series is Gevrey.\u003C\/p\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Domains of Analyticity and Gevrey estimates in weakly dissipative systems"}],"uid":"27707","created_gmt":"2021-08-10 12:39:47","changed_gmt":"2021-08-10 12:39:47","author":"Tatianna Richardson","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2021-08-27T13:00:00-04:00","event_time_end":"2021-08-27T15:00:00-04:00","event_time_end_last":"2021-08-27T15:00:00-04:00","gmt_time_start":"2021-08-27 17:00:00","gmt_time_end":"2021-08-27 19:00:00","gmt_time_end_last":"2021-08-27 19:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"221981","name":"Graduate Studies"}],"categories":[],"keywords":[{"id":"100811","name":"Phd Defense"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1788","name":"Other\/Miscellaneous"}],"invited_audience":[{"id":"78761","name":"Faculty\/Staff"},{"id":"78771","name":"Public"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}