On physical measures of multi-singular hyperbolic vector fields
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866917673800040448 |
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| author | Crovisier, Sylvain Wang, Xiaodong Yang, Dawei Zhang, Jinhua |
| author_facet | Crovisier, Sylvain Wang, Xiaodong Yang, Dawei Zhang, Jinhua |
| contents | Bonatti and da Luz have introduced the class of \emph{multi-singular hyperbolic} vector fields to characterize systems whose periodic orbits and singularities do not bifurcate under perturbation (called star vector fields).
In this paper, we study the Sina\"ı-Ruelle-Bowen measures for multi-singular hyperbolic vector fields: in a $C^1$ open and $C^1$ dense subset of multi-singular hyperbolic vector fields, each {$C^\infty$} one admits \emph{finitely} many physical measures whose basins cover a \emph{full} Lebesgue measure subset of the manifold. Similar results are also obtained for $C^1$ generic multi-singular hyperbolic vector fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_03910 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On physical measures of multi-singular hyperbolic vector fields Crovisier, Sylvain Wang, Xiaodong Yang, Dawei Zhang, Jinhua Dynamical Systems Bonatti and da Luz have introduced the class of \emph{multi-singular hyperbolic} vector fields to characterize systems whose periodic orbits and singularities do not bifurcate under perturbation (called star vector fields). In this paper, we study the Sina\"ı-Ruelle-Bowen measures for multi-singular hyperbolic vector fields: in a $C^1$ open and $C^1$ dense subset of multi-singular hyperbolic vector fields, each {$C^\infty$} one admits \emph{finitely} many physical measures whose basins cover a \emph{full} Lebesgue measure subset of the manifold. Similar results are also obtained for $C^1$ generic multi-singular hyperbolic vector fields. |
| title | On physical measures of multi-singular hyperbolic vector fields |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2305.03910 |