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math.DS2025
Twisted cocycle for interval exchange transformations: Invariant structures and Lyapunov spectrum
Hesam Rajabzadeh, Pedram Safaee
This paper investigates the algebraic and dynamical properties of the twisted cocycle, a -valued cocycle defined over the toral extension of the Zorich…
math.DS2023
Nondegeneracy of the spectrum of the twisted cocycle for interval exchange transformations
Hesam Rajabzadeh, Pedram Safaee
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 reli…
math.DS2021★ 2 cited
Quantitative weak mixing for interval exchange transformations
Artur Avila, Giovanni Forni, Pedram Safaee
We establish a dichotomy for the rate of the decay of the Cesàro averages of correlations of sufficiently regular functions for typical interval exchange transformations (IET) whic…