Livšic Theorem for Matrix Cocycles Over An Axiom A Flow

Zeng Lian , Jianhua Zhang

Communications in Mathematics and Statistics ›› 2022, Vol. 10 ›› Issue (4) : 681 -704.

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Communications in Mathematics and Statistics ›› 2022, Vol. 10 ›› Issue (4) : 681 -704. DOI: 10.1007/s40304-021-00250-x
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Livšic Theorem for Matrix Cocycles Over An Axiom A Flow

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Abstract

In this paper, we prove a version of Livšic theorem for a class of matrix cocycles over a $C^2$ Axiom A flow. As a by-product, an approximative theorem on Lyapunov exponents is also obtained which assets that Lyapunov exponents of a given ergodic measure can be approximated by those of periodic measures.

Keywords

Matrix cocycles / Axiom A flow / Lyapunov exponents

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Zeng Lian,Jianhua Zhang. Livšic Theorem for Matrix Cocycles Over An Axiom A Flow. Communications in Mathematics and Statistics, 2022, 10(4): 681-704 DOI:10.1007/s40304-021-00250-x

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National Natural Science Foundation of China(11725105)

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