"Non UBC"@en . "DSpace"@en . "Hu, Huyi"@en . "2019-03-16T05:02:54Z"@en . "2018-03-22T11:10"@en . "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."@en . "https://circle.library.ubc.ca/rest/handle/2429/68806?expand=metadata"@en . "37.0"@en . "video/mp4"@en . ""@en . "Author affiliation: Michigan State University"@en . "10.14288/1.0376993"@en . "eng"@en . "Unreviewed"@en . "Vancouver : University of British Columbia Library"@en . "Banff International Research Station for Mathematical Innovation and Discovery"@en . "Attribution-NonCommercial-NoDerivatives 4.0 International"@en . "http://creativecommons.org/licenses/by-nc-nd/4.0/"@en . "Faculty"@en . "BIRS Workshop Lecture Videos (Banff, Alta)"@en . "Mathematics"@en . "Dynamical systems and ergodic theory"@en . "Probability theory and stochastic processes"@en . "Dynamical systems"@en . "Unstable entropy and pressure for partially hyperbolic systems."@en . "Moving Image"@en . "http://hdl.handle.net/2429/68806"@en .