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arXiv · 2112.12451

Uniqueness Of Ergodic Optimization Of Top Lyapunov Exponent For Typical Matrix Cocycles

Wanshan Lin·Xueting Tian
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Abstract

In this article, we consider the ergodic optimization of the top Lyapunov exponent. We prove that there is a unique maximising measure of top Lyapunov expoent for typical matrix cocyles. By using the results we obtain, we prove that in any non-uniquely ergodic minimal dynamical system, the Lyapunov-irregular points are typical for typical matrix cocyles.

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Wanshan Lin, Xueting Tian. 2021-12-23. Uniqueness Of Ergodic Optimization Of Top Lyapunov Exponent For Typical Matrix Cocycles. https://arxiv.org/abs/2112.12451

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