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A Livšic Theorem for Matrix Cocycles Over Non-uniformly Hyperbolic Systems
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Journal Article
A Livšic Theorem for Matrix Cocycles Over Non-uniformly Hyperbolic Systems
2019
Overview
We prove a Livšic-type theorem for Hölder continuous and matrix-valued cocycles over non-uniformly hyperbolic systems. More precisely, we prove that whenever (f,μ) is a non-uniformly hyperbolic system and A:M→GL(d,R) is an α -Hölder continuous map satisfying A(fn-1(p))…A(p)=Id for every p∈Fix(fn) and n∈N , there exists a measurable map P:M→GL(d,R) satisfying A(x)=P(f(x))P(x)-1 for μ -almost every x∈M . Moreover, we prove that whenever the measure μ has local product structure the transfer map P is α -Hölder continuous in sets with arbitrary large measure.
Publisher
Springer Nature B.V
Subject
