Nondegeneracy of the spectrum of the twisted cocycle for interval exchange transformations

2023/09/11 by Hesam Rajabzadeh, Rajabzadeh, Hesam, Pedram Safaee +1
Mathematics · Physics and Astronomy · #30F60 #37A25 #37D25 #37E05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2309.05175

openalex publication_date 2023/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the positivity of the top Lyapunov exponent of the twisted (spectral) cocycle, associated with IETs, with respect to a family of natural invariant measures. The proof relies on relating the top exponent to limits of exponents along families of affine invariant submanifolds of genus tending to infinity. Applications include an observation about a conjecture of Kontsevich and Zorich, a discrepancy estimate, and a formula for the lower local dimension of spectral measures.

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