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arXiv · 2504.17153

On the creation of conjugate points for thermostats

Javier Echevarría Cuesta·James Marshall Reber
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Abstract

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 $\lambda:SM\to \mathbb{R}$ for which the thermostat $(M, g, \lambda)$ 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.

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Javier Echevarría Cuesta, James Marshall Reber. 2025-04-24. On the creation of conjugate points for thermostats. https://doi.org/10.1088/1361-6544/ae5569

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