Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (2): 575-587.doi: 10.1007/s10473-022-0211-z

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Wenda ZHANG1, Zhiqiang LI2   

  1. 1. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China;
    2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
  • Received:2020-06-13 Revised:2021-05-21 Online:2022-04-25 Published:2022-04-22
  • Supported by:
    The first author is supported by a NSFC grant (11501066) and the Department of Education in Chongqing City (KJQN201900724 and KJQN202100722) in Chongqing Jiaotong University. The second author is supported by the Chongqing Key Laboratory of Analytic Mathematics and Applications.

Abstract: In this paper, we study the pressure of C1-smooth partially hyperbolic diffeomorphisms with sup-additive potentials. We give several definitions of the so called unstable (measure theoretic) pressure in terms of Bowen's picture and the capacity picture. We show that all such unstable metric pressures of a given ergodic measure equals the corresponding unstable measure theoretic entropy plus the Lyapunov exponent of the potentials with respect to the ergodic measure.

Key words: Partially hyperbolic systems, unstable measure theoretic pressure, sup-additive potentials

CLC Number: 

  • 37D35