Title: On the creation of conjugate points for thermostats Show Chinese title

Title: 关于恒温器共轭点的创建

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. Show Chinese abstract

Abstract: 设 $(M, g)$ 是一个闭定向黎曼曲面，并令 $SM$ 为其单位切丛。 我们证明了在 $\mathcal{C}^2$ 拓扑下，光滑函数族 $\lambda:SM\to \mathbb{R}$ 中使得热流 $(M, g, \lambda)$ 没有共轭点的内点集是那些使热流为投影型 Anosov 函数族的一个子集。 此外，我们还证明了如果一个可逆热流为投影型 Anosov，则其非游荡集不含共轭点。