On existence of expanding attractors with different dimensions
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911884881428480 |
|---|---|
| author | Medvedev, V. Zhuzhoma, E. |
| author_facet | Medvedev, V. Zhuzhoma, E. |
| contents | We prove that $n$-sphere $\mathbb{S}^n$, $n\geq 2$, admits structurally stable diffeomorphisms $\mathbb{S}^n\to\mathbb{S}^n$ with non-orientable expanding attractors of any topological dimension $d\in\{1,\ldots,[\frac{n}{2}]\}$ where $[x]$ is an integer part of $x$. One proves that $n$-torus $\mathbb{T}^n$, $n\geq 2$, admits structurally stable diffeomorphisms $\mathbb{T}^n\to\mathbb{T}^n$ with orientable expanding attractors of any topological dimension $1\leq q\leq n-1$. We also prove that given any closed $n$-manifold $M^n$, $n\geq 2$, and any $d\in\{1,\ldots,[\frac{n}{2}]\}$, there is an axiom A diffeomorphism $f: M^n\to M^n$ with a $d$-dimensional non-orientable expanding attractor. Similar statements hold for axiom A flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14196 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On existence of expanding attractors with different dimensions Medvedev, V. Zhuzhoma, E. Dynamical Systems 37D15, 57R50 We prove that $n$-sphere $\mathbb{S}^n$, $n\geq 2$, admits structurally stable diffeomorphisms $\mathbb{S}^n\to\mathbb{S}^n$ with non-orientable expanding attractors of any topological dimension $d\in\{1,\ldots,[\frac{n}{2}]\}$ where $[x]$ is an integer part of $x$. One proves that $n$-torus $\mathbb{T}^n$, $n\geq 2$, admits structurally stable diffeomorphisms $\mathbb{T}^n\to\mathbb{T}^n$ with orientable expanding attractors of any topological dimension $1\leq q\leq n-1$. We also prove that given any closed $n$-manifold $M^n$, $n\geq 2$, and any $d\in\{1,\ldots,[\frac{n}{2}]\}$, there is an axiom A diffeomorphism $f: M^n\to M^n$ with a $d$-dimensional non-orientable expanding attractor. Similar statements hold for axiom A flows. |
| title | On existence of expanding attractors with different dimensions |
| topic | Dynamical Systems 37D15, 57R50 |
| url | https://arxiv.org/abs/2405.14196 |