Thermodynamic formalism of GL₂(\ℝ)-cocycles with canonical\n holonomies

2019/09/25 by Clark Butler, Butler, Clark, Park, Kiho +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Microtubule and mitosis dynamics #Protein Structure and Dynamics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1909.11548

openalex publication_date 2019/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study singular value potentials of H "older continuous\nGL₂(\ℝ)-cocycles over hyperbolic systems whose canonical holonomies\nconverge and are H "older continuous. Such cocycles include locally constant\nGL₂(\ℝ)-cocycles as well as fiber-bunched\nGL₂(\ℝ)-cocycles. We show that singular value potentials of\nirreducible such cocycles have unique equilibrium states. Among the reducible\ncocycles, we provide a characterization for cocycles whose singular value\npotentials have more than one equilibrium states.\n

Citations

• Lyapunov exponents with multiplicity 1 for deterministic products of matrices
• Almost all cocycles over any hyperbolic system have nonvanishing Lyapunov exponents

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