The Cohomological Equation for Jointly Integrable Partially Hyperbolic Diffeomorphisms on 3-Manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908294247874560 |
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| author | Li, Wenchao Shi, Yi |
| author_facet | Li, Wenchao Shi, Yi |
| contents | For a jointly integrable partially hyperbolic diffeomorphism $f$ on a 3-manifold $M$ with virtually solvable fundamental group which satisfies Diophantine condition along the center foliation, we show that the cohomological equation $φ= u\circ f - u + c$ has a continuous solution $u$ if and only if $φ$ has trivial periodic cycle functional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00925 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Cohomological Equation for Jointly Integrable Partially Hyperbolic Diffeomorphisms on 3-Manifolds Li, Wenchao Shi, Yi Dynamical Systems For a jointly integrable partially hyperbolic diffeomorphism $f$ on a 3-manifold $M$ with virtually solvable fundamental group which satisfies Diophantine condition along the center foliation, we show that the cohomological equation $φ= u\circ f - u + c$ has a continuous solution $u$ if and only if $φ$ has trivial periodic cycle functional. |
| title | The Cohomological Equation for Jointly Integrable Partially Hyperbolic Diffeomorphisms on 3-Manifolds |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2504.00925 |