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

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.

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

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].

Sectional-hyperbolic systems

2008 ◽  
Vol 28 (5) ◽  
pp. 1587-1597 ◽  
Author(s):  
R. METZGER ◽  
C. MORALES
Keyword(s):  
Vector Fields ◽  
Hyperbolic Systems ◽  
Negative Answer ◽  
Lorenz Attractor ◽  
Closed Orbits ◽  
Higher Dimensional ◽  
Singular Sets ◽  
Uniform Hyperbolicity ◽  
Mathematical Sciences ◽  
Lorenz Attractors

AbstractWe introduce a class of vector fields onn-manifolds containing the hyperbolic systems, the singular-hyperbolic systems on 3-manifolds, the multidimensional Lorenz attractors and the robust transitive singular sets in Liet al[Robust transitive singular sets via approach of an extended linear Poincaré flow.Discrete Contin. Dyn. Syst.13(2) (2005), 239–269]. We prove that the closed orbits of a system in such a class are hyperbolic in a persistent way, a property which is false for higher-dimensional singular-hyperbolic systems. We also prove that the singularities in the robust transitive sets in Liet alare similar to those in the multidimensional Lorenz attractor. Our results will give a partial negative answer to Problem 9.26 in Bonattiet al[Dynamics Beyond Uniform Hyperbolicity. A Global Geometric and Probabilistic Perspective (Encyclopaedia of Mathematical Sciences, 102. Mathematical Physics, III). Springer, Berlin, 2005].

Sign in / Sign up

Export Citation Format

Share Document