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BIRS Workshop Lecture Videos

Unstable entropy and pressure for partially hyperbolic systems. Hu, Huyi


We study ergodic properties caused by the unstable part of partially hyperbolic systems. We define unstable metric entropy, topological entropy and pressures, and prove the corresponding variational principles. For unstable metric entropy we obtain affineness, upper semi-continuity and a version of Shannon-McMillan-Breiman theorem. We also obtain existence of Gibbs u-states, differentiability properties of unstable pressure, such as tangent functionals, Gateaux differentiability and Frechet differentiability. The results are based on joint works with Weisheng Wu, Yujun Zhu and Yongxia Hua.

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