Propagation of regularity along unstable manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910023517470720 |
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| author | Lefeuvre, Thibault Potrie, Rafael |
| author_facet | Lefeuvre, Thibault Potrie, Rafael |
| contents | Let $φ_t : M \to M$ be a flow on a smooth closed connected manifold $M$ that preserves and expands a foliation $F$. We establish a theorem of propagation of regularity along the leaves of $F$ for sections of vector bundles satisfying a transport equation involving the generator of a cocycle over $φ_t$. As a consequence, we prove a regularity result for Pollicott-Ruelle resonant states: if such state is smooth in restriction to a piece of an unstable leaf, then it is in fact smooth over the entire manifold. We also announce further applications related to joint integrability of extreme bundles of partially hyperbolic diffeomorphisms. The proofs rely on a leafwise semiclassical pseudodifferential calculus adapted to a foliated space, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14558 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Propagation of regularity along unstable manifolds Lefeuvre, Thibault Potrie, Rafael Dynamical Systems Analysis of PDEs Differential Geometry 37D10, 37D30, 58J40, 35B65, 57R30 Let $φ_t : M \to M$ be a flow on a smooth closed connected manifold $M$ that preserves and expands a foliation $F$. We establish a theorem of propagation of regularity along the leaves of $F$ for sections of vector bundles satisfying a transport equation involving the generator of a cocycle over $φ_t$. As a consequence, we prove a regularity result for Pollicott-Ruelle resonant states: if such state is smooth in restriction to a piece of an unstable leaf, then it is in fact smooth over the entire manifold. We also announce further applications related to joint integrability of extreme bundles of partially hyperbolic diffeomorphisms. The proofs rely on a leafwise semiclassical pseudodifferential calculus adapted to a foliated space, which may be of independent interest. |
| title | Propagation of regularity along unstable manifolds |
| topic | Dynamical Systems Analysis of PDEs Differential Geometry 37D10, 37D30, 58J40, 35B65, 57R30 |
| url | https://arxiv.org/abs/2602.14558 |