Uniform quasi-multiplicativity of locally constant cocycles and applications

2022/09/19 by Reza Mohammadpour, Mohammadpour, Reza, Park, Kiho · 2 citations
Mathematics · #28A80 #37A45 #37D35 #37H15 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2209.08999

openalex publication_date 2022/09/19 · openalex created_date 2022/09/21 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that a locally constant cocycle A is k-quasi multiplicative under the irreducibility assumption. More precisely, we show that if A^t and A^{\wedge m} are irreducible for every t | d and 1≤ m ≤ d-1, then A is k-uniformly spannable for some k∈ ℕ, which implies that A is k-quasi multiplicative. We apply our results to show that the unique subadditive equilibrium Gibbs state is ψ-mixing and calculate the Hausdorff dimension of cylindrical shrinking target and recurrence sets.

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• Statistical properties of equilibrium states for fiber-bunched matrix cocycles and applications
• Non-unique equilibrium measures and freezing phase transitions for matrix cocycles for negative t

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