Upper semi-continuity of entropy map for nonuniformly hyperbolic systems

Nonlinearity ◽  
2015 ◽  
Vol 28 (8) ◽  
pp. 2977-2992 ◽  
Author(s):  
Gang Liao ◽  
Wenxiang Sun ◽  
Shirou Wang
Keyword(s):  
Hyperbolic Systems ◽  
Nonuniformly Hyperbolic

scholarly journals A note on statistical properties for nonuniformly hyperbolic systems with slow contraction and expansion

2016 ◽  
Vol 16 (03) ◽  
pp. 1660012 ◽  
Author(s):  
Ian Melbourne ◽  
Paulo Varandas
Keyword(s):  
Invariance Principle ◽  
Hyperbolic Systems ◽  
Return Time ◽  
Limit Laws ◽  
Weak Invariance Principle ◽  
Weak Invariance ◽  
The Central Limit Theorem ◽  
Statistical Limit ◽  
Contraction And Expansion ◽  
Nonuniformly Hyperbolic

We provide a systematic approach for deducing statistical limit laws via martingale-coboundary decomposition, for nonuniformly hyperbolic systems with slowly contracting and expanding directions. In particular, if the associated return time function is square-integrable, then we obtain the central limit theorem, the weak invariance principle, and an iterated version of the weak invariance principle.

scholarly journals On the uniform hyperbolicity of some nonuniformly hyperbolic systems

2002 ◽  
Vol 131 (4) ◽  
pp. 1303-1309 ◽  
Author(s):  
José F. Alves ◽  
Vítor Araújo ◽  
Benoît Saussol
Keyword(s):  
Hyperbolic Systems ◽  
Uniform Hyperbolicity ◽  
Nonuniformly Hyperbolic

Livšic theorem for matrix cocycles over nonuniformly hyperbolic systems

2019 ◽  
Vol 19 (02) ◽  
pp. 1950010 ◽  
Author(s):  
Rui Zou ◽  
Yongluo Cao
Keyword(s):  
Periodic Point ◽  
Measurable Function ◽  
Hyperbolic Systems ◽  
Type Theorem ◽  
Hölder Continuous ◽  
Nonuniformly Hyperbolic

We prove a nonuniformly hyperbolic version of the Livšic-type theorem, with cocycles taking values in [Formula: see text]. To be more precise, let [Formula: see text] Diff[Formula: see text] preserving an ergodic hyperbolic measure [Formula: see text], and [Formula: see text] be Hölder continuous satisfying [Formula: see text] for each periodic point [Formula: see text], then there exists a measurable function [Formula: see text] satisfying [Formula: see text] for [Formula: see text]-almost every [Formula: see text].

scholarly journals Large deviations for nonuniformly hyperbolic systems

2008 ◽  
Vol 360 (12) ◽  
pp. 6661-6676 ◽  
Author(s):  
Ian Melbourne ◽  
Matthew Nicol
Keyword(s):  
Large Deviations ◽  
Hyperbolic Systems ◽  
Nonuniformly Hyperbolic

scholarly journals Nonuniformly hyperbolic systems arising from coupling of chaotic and gradient-like systems

2020 ◽  
Vol 40 (10) ◽  
pp. 6015-6041
Author(s):  
Matteo Tanzi ◽  
◽  
Lai-Sang Young ◽  
Keyword(s):  
Hyperbolic Systems ◽  
Nonuniformly Hyperbolic
Sign in / Sign up

Export Citation Format

Share Document