Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points

Gerhard Knieper; Khadim War; Vaughn Climenhaga

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arxiv 1903.09831 v2 pith:77CQHIXN submitted 2019-03-23 math.DS math.DG

Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points

Vaughn Climenhaga , Gerhard Knieper , Khadim War This is my paper

classification math.DS math.DG

keywords measureconjugateentropyflowgeodesicmaximalpointswithout

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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.

Uniqueness of the measure of maximal entropy for geodesic flows on certain manifolds without conjugate points

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