BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Robert Szczelina (Jagiellonian University\, Poland)
DTSTART:20210112T150000Z
DTEND:20210112T160000Z
DTSTAMP:20260423T024723Z
UID:CRM-CAMP/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRM-CAMP/27/
 ">A computer assisted proof of chaos in a delayed perturbation of chaotic 
 ODE</a>\nby Robert Szczelina (Jagiellonian University\, Poland) as part of
  CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analysis\n\
 n\nAbstract\nWe will discuss some recent developments to the Taylor method
  for forward in time rigorous integration of Delay Differential Equations 
 (DDEs) with constant delays. We briefly discuss how to generalize method o
 f the paper "Algorithm for rigorous integration of Delay Differential Equa
 tions and the computer-assisted proof of periodic orbits in the Mackey-Gla
 ss equation\, Found. Comp. Math.\, 18 (6)\, 1299-1332\, 2018" to incorpora
 te multiple lags\, multiple variables (systems of equations) and how to ut
 ilize "smoothing of solutions" to produce results of a far greater accurac
 y\, especially when computing Poincaré maps between local sections. We wi
 ll apply this method to validate some covering relations between carefully
  selected sets under Poincaré maps defined with a flow associated to a DD
 E. Together with standard topological arguments for compact maps it will p
 rove existence of a chaotic dynamics\, in particular the existence of infi
 nite (countable) number of periodic orbits. The DDE under consideration is
  a toy example made by adding a delayed term to the Rössler ODE under par
 ameters for which chaotic attractor exists. The delayed term is small in a
 mplitude\, but the lag time is macroscopic (not small). This is a joint wo
 rk with Piotr Zgliczyński.\n
LOCATION:https://researchseminars.org/talk/CRM-CAMP/27/
END:VEVENT
END:VCALENDAR