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

Hesam Rajabzadeh; Pedram Safaee

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

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arxiv 2309.05175 v1 pith:NWLLEISM submitted 2023-09-11 math.DS

Hesam Rajabzadeh , Pedram Safaee This is my paper · ORCID

classification math.DS

keywords cocycleexponentinvariantmeasuresspectraltwistedaffinealong

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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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Twisted cocycle for interval exchange transformations: Invariant structures and Lyapunov spectrum
math.DS 2025-01 conditional novelty 8.0 of 10

The twisted cocycle over interval exchange renormalizations has a symmetric Lyapunov spectrum with at least κ+1 zero exponents, and is fully degenerate for rotation-type permutations on their homology torus.

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