Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential

2001/10/31 by Jean Bourgain, J. Bourgain, Bourgain, J. +3 · 2 citations
Mathematics · Physics and Astronomy · #37D25 #81Q99 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.DS #math.MP #msc:37D25 #msc:81Q99

paper · pdf · doi:10.48550/arxiv.math-ph/0110040

arxiv created 2001/10/31 · openalex publication_date 2001/10/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study regularity properties of the Lyapunov exponent L of quasiperiodic operators with analytic potential, under no assumptions on the Diophantine class of the frequency. We prove that L is jointly continuous, in frequency and energy, at every irrational frequency.

Citations

• Holder Continuity of the Integrated Density of States for Quasi-Periodic Schrodinger Equations and Averages of Shifts of Subharmonic Functions

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• Discontinuity of Lyapunov exponent in spaces of quasiperiodic cocycles: Smoothness vs Arithmetic
• Schrödinger operators with dynamically defined potentials

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