論文

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2023年6月16日

Historic and physical wandering domains for wild blender-horseshoes

Nonlinearity
  • Shin Kiriki
  • ,
  • Yushi Nakano
  • ,
  • Teruhiko Soma

36
8
開始ページ
4007
終了ページ
4033
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1088/1361-6544/acda74

We give a contribution to Takens' last problem [Tak08] in the $C^{1}$
topology (note that solutions have been already given in the smooth category of
more than or equal to $C^{2}$, see [KS17,BB]). To be specific, we present a
one-parameter family $\mathscr{A}$ of $C^1$ diffeomorphisms having wild
blender-horseshoes such that every $C^1$ neighbourhood of any element of
$\mathscr{A}$ contains two types of diffeomorphisms, one of which has a
historic contracting wandering domain, and the other has a non-trivial Dirac
physical measure associated with a contracting wandering domain. It is a
non-trivial extension of Colli-Vargas' model [CV01] to the higher dimensional
dynamics with the use of wild blender-horseshoes.

リンク情報
DOI
https://doi.org/10.1088/1361-6544/acda74
arXiv
http://arxiv.org/abs/arXiv:2107.09844
URL
http://arxiv.org/abs/2107.09844v1
URL
http://arxiv.org/pdf/2107.09844v1 本文へのリンクあり
Scopus
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85163287308&origin=inward
Scopus Citedby
https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85163287308&origin=inward
ID情報
  • DOI : 10.1088/1361-6544/acda74
  • ISSN : 0951-7715
  • eISSN : 1361-6544
  • arXiv ID : arXiv:2107.09844
  • SCOPUS ID : 85163287308

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