Entropy of Lyapunov maximizing measures of SL(2,ℝ) typical cocycles

2021/09/01 by Mohammadpour, Reza
#15B48 #37D30 #37H15 #93C30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.00469

Abstract

In this paper we study ergodic optimization problems for typical cocycles. We consider one-step SL(2,ℝ)-cocycles that satisfy pinching and twisting conditions. We prove that the Lyapunov maximizing measures have zero entropy under additional assumptions that the maps e₁ and e₂ are one-to-one on the Mather set.

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