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SUMMARY:Artem Dudko (Institute of Mathematics\, Polish Academy of Sciences
 )
DTSTART:20261015T140000Z
DTEND:20261015T153000Z
DTSTAMP:20261026T214405Z
UID:fran/88
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/fran/88/">On
  attractors of Fibonacci maps</a>\nby Artem Dudko (Institute of Mathematic
 s\, Polish Academy of Sciences) as part of Семінар з фракта
 льного аналізу / Fractal analysis seminar\n\n\nAbstract\nIn 1
 990s Henk Bruin\, Gerhard Keller\, Tomasz Nowicki\, and Sebastian van Stri
 en showed that smooth unimodal maps with Fibonacci combinatorics and suffi
 ciently high degree of a critical point have a wild attractor\, i.e. their
  metric and topological attractors do not coincide. However\, until recent
 ly there were no reasonable estimates on the degree of the critical point 
 needed.\n\nIn the talk I will present a constructive approach for studying
  attractors of maps\, which are periodic points of a renormalization. Usin
 g this approach and rigorous computer estimates\, we show that the Fibonac
 ci map of degree $d = 3.8$ does not have a wild attractor\, but that for d
 egree $d = 5.1$ the wild attractor exists.\n\nThe talk is based on a joint
  work with Denis Gaidashev.\n
LOCATION:https://researchseminars.org/talk/fran/88/
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