Unstable metric pressure of partially hyperbolic diffeomorphisms with sub-additive potentials. (21st October 2020)

• Record Type: Journal Article
• Authors: Zhang, Wenda; Li, Zhiqiang; Zhou, Yunhua
• Is Part Of: Nonlinearity. Volume 33:Number 12(2020)
• Page Start: 6915
• Page End: 6934
• Publication Date: 2020-10-21
• Subjects: unstable measure theoretic pressure -- sub-additive potential -- variational principle; Primary 37D35 -- Secondary 37D30; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aba966
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper, we define and study unstable measure theoretic pressure for C 1 -smooth partially hyperbolic diffeomorphisms with sub-additive potentials. We show that this measure theoretic pressure for any ergodic measure equals the corresponding unstable measure theoretic entropy plus the Lyapunov exponent of the potentials with respect to the ergodic measure. On the other hand, we also give other definitions of unstable metric pressure, in terms of Bowen's picture and the capacity picture. We show that all definitions of unstable metric pressure, including the one defined at the beginning, actually coincide for any ergodic measure.