A characterization of physical measures for systems with mixed central behavior
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913882128252928 |
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| author | Araujo, Vitor Salgado, Luciana |
| author_facet | Araujo, Vitor Salgado, Luciana |
| contents | We show that the existence of physical measures for $C^\infty$ smooth instances of certain partially hyperbolic dynamics, both continuous and discrete, exhibiting mixed behavior (positive and negative Lyapunov exponents) along the central non-uniformly hyperbolic multidimensional invariant direction, is equivalent to the existence of certain types of ``regular points'' on positive volume subsets, including Lyapunov regular points. This encompasses the $C^3$ robust class of multidimensional non-hyperbolic attractors obtained by Viana, and the $C^1$ robust classes of $3$-sectionally hyperbolic wild strange attractors presented by Shilnikov and Turaev, providing necessary and sufficient conditions for the existence of ergodic hyperbolic physical measures on these and other dynamical systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_10144 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A characterization of physical measures for systems with mixed central behavior Araujo, Vitor Salgado, Luciana Dynamical Systems 37D45, 37D30, 37D25, 37D35 We show that the existence of physical measures for $C^\infty$ smooth instances of certain partially hyperbolic dynamics, both continuous and discrete, exhibiting mixed behavior (positive and negative Lyapunov exponents) along the central non-uniformly hyperbolic multidimensional invariant direction, is equivalent to the existence of certain types of ``regular points'' on positive volume subsets, including Lyapunov regular points. This encompasses the $C^3$ robust class of multidimensional non-hyperbolic attractors obtained by Viana, and the $C^1$ robust classes of $3$-sectionally hyperbolic wild strange attractors presented by Shilnikov and Turaev, providing necessary and sufficient conditions for the existence of ergodic hyperbolic physical measures on these and other dynamical systems. |
| title | A characterization of physical measures for systems with mixed central behavior |
| topic | Dynamical Systems 37D45, 37D30, 37D25, 37D35 |
| url | https://arxiv.org/abs/2405.10144 |