Livšic Theorem for Matrix Cocycles Over An Axiom A Flow

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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Funding

National Natural Science Foundation of China(11725105)