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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2409.01798 |
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| _version_ | 1866915802071957504 |
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| author | Bochi, Jairo Pesin, Yakov Sarig, Omri |
| author_facet | Bochi, Jairo Pesin, Yakov Sarig, Omri |
| contents | Given a continuous linear cocycle A over a homeomorphism f of a compact metric space X, we investigate its set R of Lyapunov-Perron regular points, that is, the collection of trajectories of f that obey the conclusions of the Multiplicative Ergodic Theorem. We obtain results roughly saying that the set R is of first Baire category (i.e., meager) in X, unless some rigid structure is present. In some settings, this rigid structure forces the Lyapunov exponents to be defined everywhere and to be independent of the point; that is what we call complete regularity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01798 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complete regularity of linear cocycles and the Baire category of the set of Lyapunov-Perron regular points Bochi, Jairo Pesin, Yakov Sarig, Omri Dynamical Systems 37D25, 37D30 Given a continuous linear cocycle A over a homeomorphism f of a compact metric space X, we investigate its set R of Lyapunov-Perron regular points, that is, the collection of trajectories of f that obey the conclusions of the Multiplicative Ergodic Theorem. We obtain results roughly saying that the set R is of first Baire category (i.e., meager) in X, unless some rigid structure is present. In some settings, this rigid structure forces the Lyapunov exponents to be defined everywhere and to be independent of the point; that is what we call complete regularity. |
| title | Complete regularity of linear cocycles and the Baire category of the set of Lyapunov-Perron regular points |
| topic | Dynamical Systems 37D25, 37D30 |
| url | https://arxiv.org/abs/2409.01798 |