Transitivity of real Anosov diffeomorphisms
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909951228641280 |
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| author | Carvalho, Bernardo |
| author_facet | Carvalho, Bernardo |
| contents | We prove the transitivity of real Anosov diffeomorphisms, which are Anosov diffeomorphisms where stable and unstable spaces decompose into a continuous sum of invariant one-dimensional sub-spaces with uniform contraction/expansion over the ambient manifold. We prove that if a stable/unstable curve has a well-defined length in a conformal hyperbolic distance, then it has a globally defined holonomy. We exhibit a conformal hyperbolic distance with well-defined length of stable/unstable curves for each real Anosov diffeomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_15740 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transitivity of real Anosov diffeomorphisms Carvalho, Bernardo Dynamical Systems Differential Geometry We prove the transitivity of real Anosov diffeomorphisms, which are Anosov diffeomorphisms where stable and unstable spaces decompose into a continuous sum of invariant one-dimensional sub-spaces with uniform contraction/expansion over the ambient manifold. We prove that if a stable/unstable curve has a well-defined length in a conformal hyperbolic distance, then it has a globally defined holonomy. We exhibit a conformal hyperbolic distance with well-defined length of stable/unstable curves for each real Anosov diffeomorphism. |
| title | Transitivity of real Anosov diffeomorphisms |
| topic | Dynamical Systems Differential Geometry |
| url | https://arxiv.org/abs/2410.15740 |