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The set of points with Markovian symbolic dynamics for non-uniformly hyperbolic diffeomorphisms
Ergodic Theory and Dynamical Systems ( IF 0.9 ) Pub Date : 2020-11-04 , DOI: 10.1017/etds.2020.114
SNIR BEN OVADIA

The papers [O. M. Sarig. Symbolic dynamics for surface diffeomorphisms with positive entropy. J. Amer. Math. Soc.26(2) (2013), 341–426] and [S. Ben Ovadia. Symbolic dynamics for non-uniformly hyperbolic diffeomorphisms of compact smooth manifolds. J. Mod. Dyn.13 (2018), 43–113] constructed symbolic dynamics for the restriction of $C^r$ diffeomorphisms to a set $M'$ with full measure for all sufficiently hyperbolic ergodic invariant probability measures, but the set $M'$ was not identified there. We improve the construction in a way that enables $M'$ to be identified explicitly. One application is the coding of infinite conservative measures on the homoclinic classes of Rodriguez-Hertz et al. [Uniqueness of SRB measures for transitive diffeomorphisms on surfaces. Comm. Math. Phys.306(1) (2011), 35–49].

中文翻译:

非均匀双曲微分同胚的马尔可夫符号动力学点集

论文 [OM Sarig。具有正熵的表面微分同胚的符号动力学。J.阿米尔。数学。社会党。26(2) (2013), 341–426] 和 [S. 本·奥瓦迪亚。紧致光滑流形的非均匀双曲微分同胚的符号动力学。J.国防部。达因。13(2018), 43–113] 构建了符号动力学来限制$C^r$对集合的微分同胚$M'$对所有足够双曲的遍历不变概率测度具有完整测度,但集合$M'$在那里没有被发现。我们以一种能够使$M'$要明确标识。一种应用是对 Rodriguez-Hertz 同宿类的无限保守度量进行编码等。[表面上传递微分同胚的 SRB 度量的唯一性。通讯。数学。物理。306(1) (2011), 35–49]。
更新日期:2020-11-04
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