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DTSTAMP:20260720T052712Z
SUMMARY:Shin Kiriki (Tokai University): Takens’ last problem and existenc
 e of non-trivial wandering domains
DESCRIPTION:We give an answer to the last open problem of F. Takens 2008 wh
 ich is related to “historic behavior” of dynamical systems. For this p
 urpose\, existence of non-trivial wandering domains near a homoclinic tang
 ency has a significant role\, which is conjectured by E. Colli and E.Varga
 s 2001. Concretely speaking\, we show that any Newhouse open set in the $C
 ^{infty}$ topology of two-dimensional diffeomorphisms is contained in the 
 closure of the set of diffeomorphisms which have wandering domains whose f
 orward orbits have historic behavior. Moreover\, this result implies an an
 swer in the $C^{infty}$ category to one of the open problems of S. van Str
 ien 2010 which is concerned with wandering domains for H’enon family. Th
 is study is a joint research with Soma Teruhiko.
URL:https://www.imperial.ac.uk/events/104665/shin-kiriki-tokai-university-t
 akens-last-problem-and-existence-of-non-trivial-wandering-domains/
DTSTART;TZID=Europe/London:20150312T140000
DTEND;TZID=Europe/London:20150312T150000
LOCATION:United Kingdom
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