We prove that for closed surfaces $M$ with Riemannian metrics without conjugate points and genus $\geq 2$ the geodesic flow on the unit tangent bundle $T^1M$ has a unique measure of maximal entropy. Furthermore, this measure is fully supported on $T^1M$ and the flow is mixing with respect to this measure. We formulate conditions under which this result extends to higher dimensions.

中文翻译：

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某些没有共轭点的流形上测地线流的最大熵度量的唯一性

我们证明，对于没有共轭点和属 $\geq 2$ 的黎曼度量的闭合曲面 $M$，单位切线丛 $T^1M$ 上的测地线流具有最大熵的唯一度量。此外，该措施在 $T^1M$ 上得到完全支持，并且与该措施相关的流量正在混合。我们制定了将结果扩展到更高维度的条件。