BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Daniel Wilczak (Jagiellonian University) DTSTART:20200804T140000Z DTEND:20200804T150000Z DTSTAMP:20260423T024701Z UID:CRM-CAMP/6 DESCRIPTION:Title: Rigorous numerical investigation of chaos and stability of periodic orbit s in the Kuramoto-Sivashinsky PDE\nby Daniel Wilczak (Jagiellonian Uni versity) as part of CRM CAMP (Computer-Assisted Mathematical Proofs) in No nlinear Analysis\n\n\nAbstract\nWe give a computer-assisted proof of the e xistence of symbolic dynamics for a certain Poincaré map in the one-dimen sional Kuramoto-Sivashinsky PDE. In particular\, we show the existence of infinitely many (countably) periodic orbits (POs) of arbitrary large princ ipal periods. We provide also a study of the stability type of some POs. T he proof utilizes pure topological results (variant of the method of cover ing relations on compact absolute neighbourhood retracts) with rigorous in tegration of the PDE and the associated variational equation. This talk is based on the recent results [1\,2].\n\n[1] D. Wilczak and P. Zgliczyński . A geometric method for infinite-dimensional chaos: symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line\, Journal of Differential Equati ons\, Vol. 269 No. 10 (2020)\, 8509-8548.\n\n[2] D. Wilczak and P. Zgliczy ński. A rigorous C1-algorithm for integration of dissipative PDEs based o n automatic differentiation and the Taylor method\, in preparation.\n LOCATION:https://researchseminars.org/talk/CRM-CAMP/6/ END:VEVENT END:VCALENDAR