2023年6月16日
Historic and physical wandering domains for wild blender-horseshoes
Nonlinearity
- ,
- ,
- 巻
- 36
- 号
- 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.
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