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Published on May 9, 2019
Palestra Especial: Measure of maximal entropy for geodesic flows on surfaces without conjugate points Khadim War - IMPA
Abstract: In this talk we first give a general overview on the properties of the measure of maximal entropy (MME) for geodesic flows on surfaces with negative curvature. We will show how these properties extend to the case of metric without conjugate pionts. In particual, in the case of surfaces without conjugate points, we prove that the MME is unique, fully supported, can be obtained from limiting distribution along closed orbits and the flow is mixing with respect to it. As a consequence we have that the closed orbits are dense in the unit tangent bundle. We also formulate conditions under which these results generalise to higher dimension. This is based on a joint work with Vaughn Climenhaga and Gerhard Knieper.