Upper bound on the regularity of the Lyapunov exponent for random products of matrices

2022/08/06 by Jamerson Bezerra, Pedro Duarte, Bezerra, Jamerson +1 · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.2208.03575

Abstract

We prove that if μ is a finitely supported measure on SL₂(ℝ) with positive Lyapunov exponent but not uniformly hyperbolic, then the Lyapunov exponent function is not α-Hölder around μ for any α exceeding the Shannon entropy of μ over the Lyapunov exponent of μ.

Cited by

• Obstructions to the regularity of the Lyapunov exponents for non-compact random Schrödinger cocycles

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