Preimage pressure, stable pressure and equilibrium states

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Li, Zhiming¹  Wu, Weisheng²  Zhu, Yujun³ 

[1] Northwest Univ, Sch Math, Xian 710127, Peoples R China

[2] China Agr Univ, Coll Sci, Dept Appl Math, Beijing 100083, Peoples R China

[3] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

关键词: Pointwise preimage pressures;    Stable pressures;    Variational principles;    Equilibrium states;   

DOI  :  10.1016/j.jde.2020.04.043

来源: Elsevier

【 摘 要 】

In this paper, the pressure of a potential via the dynamics of preimage structure are investigated for non-invertible systems and the properties for the related equilibrium states are considered. For a continuous map on a compact metric space, a notion of preimage pressure via the preimages of single points is introduced, and then some fundamental properties are considered and a variational principle is established for the system with uniform separation of preimages. For a C-1-partially hyperbolic endomorphism on a closed Riemannian manifold, a notion of stable pressure via the preimages of local stable manifolds is introduced and a corresponding variational principle is established. Moreover, equilibrium states and tangent functionals for pointwise preimage pressures and stable pressures are also considered. By describing the set of equilibrium states and tangent functionals and a sense of continuous dependence of equilibrium states with respect to the potential, we prove that the continuous potentials with unique equilibrium state form a dense G(delta) set. In addition, for any finite collection of ergodic measures, we can find a continuous potential such that its set of equilibrium states contains the given set. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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