Entropy of Lyapunov maximizing measures of $SL(2,\mathbb{R})$ typical cocycles

Reza Mohammadpour

Entropy of Lyapunov maximizing measures of $SL(2,\mathbb{R})$ typical cocycles

Dynamical Systems 2025-01-09 v4

Authors: Reza Mohammadpour

Abstract

In this paper we study ergodic optimization problems for typical cocycles. We consider one-step $SL(2,\mathbb{R})$ -cocycles that satisfy pinching and twisting conditions. We prove that the Lyapunov maximizing measures have zero entropy under additional assumptions that the maps $e_1$ and $e_2$ are one-to-one on the Mather set.

Keywords

ergodic optimization sl(2,r) cocycles lyapunov maximizing measures zero entropy pinching and twisting

Cite

@article{arxiv.2109.00469,
  title  = {Entropy of Lyapunov maximizing measures of $SL(2,\mathbb{R})$ typical cocycles},
  author = {Reza Mohammadpour},
  journal= {arXiv preprint arXiv:2109.00469},
  year   = {2025}
}

Comments

Some examples were added, and typos were corrected. To appear in Dynamical Systems: An International Journal

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