Marked magnetic action rigidity
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915927405101056 |
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| author | Beaufort, Louis-Brahim Muñoz-Thon, Sebastián Richardson, Sean |
| author_facet | Beaufort, Louis-Brahim Muñoz-Thon, Sebastián Richardson, Sean |
| contents | An exact magnetic system over a closed manifold $M$ consists of a pair $(g,α)$, where $g$ is a Riemannian metric and $α$ is a 1-form encoding a magnetic field. In this context, we consider a generalization of the marked length rigidity conjecture: does the marked magnetic action spectrum of magnetic systems with Anosov magnetic flow determine the metric and the 1-form, up to a natural obstruction? In this article we answer this question in two settings: 1) locally for systems with close metrics and 1-forms and 2) for metrics in the same conformal class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08262 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Marked magnetic action rigidity Beaufort, Louis-Brahim Muñoz-Thon, Sebastián Richardson, Sean Dynamical Systems Differential Geometry 37D20, 37D40 An exact magnetic system over a closed manifold $M$ consists of a pair $(g,α)$, where $g$ is a Riemannian metric and $α$ is a 1-form encoding a magnetic field. In this context, we consider a generalization of the marked length rigidity conjecture: does the marked magnetic action spectrum of magnetic systems with Anosov magnetic flow determine the metric and the 1-form, up to a natural obstruction? In this article we answer this question in two settings: 1) locally for systems with close metrics and 1-forms and 2) for metrics in the same conformal class. |
| title | Marked magnetic action rigidity |
| topic | Dynamical Systems Differential Geometry 37D20, 37D40 |
| url | https://arxiv.org/abs/2604.08262 |