Smooth orbit equivalence rigidity for dissipative geodesic flows
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914252644679680 |
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| author | Cuesta, Javier Echevarría |
| author_facet | Cuesta, Javier Echevarría |
| contents | Let $M$ be a smooth closed oriented surface. Gaussian thermostats on $M$ correspond to the geodesic flows arising from metric connections, including those with non-zero torsion. These flows may not preserve any absolutely continuous measure. We prove that if two Gaussian thermostats on $M$ with negative thermostat curvature are related by a smooth orbit equivalence isotopic to the identity, then the two background metrics are conformally equivalent via a smooth diffeomorphism of $M$ isotopic to the identity. We also give a relationship between the thermostat forms themselves. Finally, we prove the same result for Anosov magnetic flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Smooth orbit equivalence rigidity for dissipative geodesic flows Cuesta, Javier Echevarría Dynamical Systems Differential Geometry 37D40 (Primary) 37C15, 53C24 (Secondary) Let $M$ be a smooth closed oriented surface. Gaussian thermostats on $M$ correspond to the geodesic flows arising from metric connections, including those with non-zero torsion. These flows may not preserve any absolutely continuous measure. We prove that if two Gaussian thermostats on $M$ with negative thermostat curvature are related by a smooth orbit equivalence isotopic to the identity, then the two background metrics are conformally equivalent via a smooth diffeomorphism of $M$ isotopic to the identity. We also give a relationship between the thermostat forms themselves. Finally, we prove the same result for Anosov magnetic flows. |
| title | Smooth orbit equivalence rigidity for dissipative geodesic flows |
| topic | Dynamical Systems Differential Geometry 37D40 (Primary) 37C15, 53C24 (Secondary) |
| url | https://arxiv.org/abs/2406.00607 |