Work

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

Year: 2025

Type: article

Abstract: We prove the positivity of the top Lyapunov exponent of the twisted (spectral) cocycle, associated with interval exchange transformations (IETs), with respect to a family of natural invariant measures. The proof relies on relating the top exponent to the limit of exponents of the Kontsevich–Zorich cocycle 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.

Source: Journal of the European Mathematical Society

DOI: 10.4171/jems/1687

Authors: Hesam Rajabzadeh, Pedram Safaee

Institutions: Institute for Research in Fundamental Sciences, École Polytechnique, University of Zurich

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4413381833

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