The C1+α hypothesis in Pesin theory

1984 ◽  
Vol 59 (1) ◽  
pp. 143-161 ◽  
Author(s):  
Charles C. Pugh
Keyword(s):  
Pesin Theory

scholarly journals Dominated Pesin theory: convex sum of hyperbolic measures

2018 ◽  
Vol 226 (1) ◽  
pp. 387-417 ◽  
Author(s):  
Jairo Bochi ◽  
Christian Bonatti ◽  
Katrin Gelfert
Keyword(s):  
Pesin Theory

scholarly journals Large-deviation properties in some non-uniformly hyperbolic systems via Pesin theory

2016 ◽  
Vol 31 (4) ◽  
pp. 483-495
Author(s):  
Zheng Yin ◽  
Ercai Chen
Keyword(s):  
Large Deviation ◽  
Hyperbolic Systems ◽  
Pesin Theory ◽  
Uniformly Hyperbolic Systems

scholarly journals Pesin theory and equilibrium measures on the interval

2015 ◽  
Vol 231 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Neil Dobbs
Keyword(s):  
Equilibrium Measures ◽  
Pesin Theory

scholarly journals Quantitative Pesin theory for Anosov diffeomorphisms and flows

2017 ◽  
Vol 39 (1) ◽  
pp. 159-200
Author(s):  
SÉBASTIEN GOUËZEL ◽  
LUCHEZAR STOYANOV
Keyword(s):  
Dynamical System ◽  
Anosov Diffeomorphisms ◽  
Exponential Mixing ◽  
Hyperbolic Dynamics ◽  
Pesin Theory ◽  
Anosov Flows ◽  
Exponentially Small

Pesin sets are measurable sets along which the behavior of a matrix cocycle above a measure-preserving dynamical system is explicitly controlled. In uniformly hyperbolic dynamics, we study how often points return to Pesin sets under suitable conditions on the cocycle: if it is locally constant, or if it admits invariant holonomies and is pinching and twisting, we show that the measure of points that do not return a linear number of times to Pesin sets is exponentially small. We discuss applications to the exponential mixing of contact Anosov flows and consider counterexamples illustrating the necessity of suitable conditions on the cocycle.

scholarly journals The $C^{1+\alpha }$ hypothesis in Pesin Theory revisited

2013 ◽  
Vol 7 (4) ◽  
pp. 605-618 ◽  
Author(s):  
Christian Bonatti ◽  
◽  
Sylvain Crovisier ◽  
Katsutoshi Shinohara ◽  
◽  
...  
Keyword(s):  
Pesin Theory
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