Partially hyperbolic diffeormorphisms, ergodicity, and transverse foliations in dimension 3
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| Format: | Preprint |
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2025
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| _version_ | 1866914098011176960 |
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| author | Fenley, S. R. Potrie, R. |
| author_facet | Fenley, S. R. Potrie, R. |
| contents | We give a complete topological classification of transitive partially hyperbolic diffeomorphisms in 3-manifolds in terms of Anosov flows, completing a program proposed by Pujals. In particular, this also allows to give a full answer to the ergodicity conjecture of Hertz-Hertz-Ures for partially hyperbolic diffeomorphisms in dimension 3. This is achieved by showing a general result about pairs of transverse $2$-dimensional foliations in 3-manifolds with Gromov hyperbolic leaves which may be of independent interest. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_15176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Partially hyperbolic diffeormorphisms, ergodicity, and transverse foliations in dimension 3 Fenley, S. R. Potrie, R. Dynamical Systems Geometric Topology We give a complete topological classification of transitive partially hyperbolic diffeomorphisms in 3-manifolds in terms of Anosov flows, completing a program proposed by Pujals. In particular, this also allows to give a full answer to the ergodicity conjecture of Hertz-Hertz-Ures for partially hyperbolic diffeomorphisms in dimension 3. This is achieved by showing a general result about pairs of transverse $2$-dimensional foliations in 3-manifolds with Gromov hyperbolic leaves which may be of independent interest. |
| title | Partially hyperbolic diffeormorphisms, ergodicity, and transverse foliations in dimension 3 |
| topic | Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2510.15176 |