On the creation of conjugate points for thermostats
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908955690663936 |
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| author | Cuesta, Javier Echevarría Reber, James Marshall |
| author_facet | Cuesta, Javier Echevarría Reber, James Marshall |
| contents | Let $(M, g)$ be a closed oriented Riemannian surface, and let $SM$ be its unit tangent bundle. We show that the interior in the $\mathcal{C}^2$ topology of the set of smooth functions $λ:SM\to \mathbb{R}$ for which the thermostat $(M, g, λ)$ has no conjugate points is a subset of those functions for which the thermostat is projectively Anosov. Moreover, we prove that if a reversible thermostat is projectively Anosov, then its non-wandering set contains no conjugate points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_17153 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the creation of conjugate points for thermostats Cuesta, Javier Echevarría Reber, James Marshall Dynamical Systems Differential Geometry 37D30 (Primary) 37C10 (Secondary) Let $(M, g)$ be a closed oriented Riemannian surface, and let $SM$ be its unit tangent bundle. We show that the interior in the $\mathcal{C}^2$ topology of the set of smooth functions $λ:SM\to \mathbb{R}$ for which the thermostat $(M, g, λ)$ has no conjugate points is a subset of those functions for which the thermostat is projectively Anosov. Moreover, we prove that if a reversible thermostat is projectively Anosov, then its non-wandering set contains no conjugate points. |
| title | On the creation of conjugate points for thermostats |
| topic | Dynamical Systems Differential Geometry 37D30 (Primary) 37C10 (Secondary) |
| url | https://arxiv.org/abs/2504.17153 |