Ergodicity of skew-products over typical IETs

2024/05/13 by Argentieri, Fernando, Berk, Przemysław, Trujillo, Frank
#37A40 #37E05 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.07645

Abstract

We prove ergodicity of a class of infinite measure preserving systems, called skew-products. More precisely, we consider systems of the form T_f:[0, 1) × ℝ→[0, 1) × ℝ, T_f(x, t):=(T(x), t+f(x)), where T is an interval exchange transformation and f is a piece-wise constant function with a finite number of discontinuities. We show that such system is ergodic with respect to Leb_{[0,1)× ℝ} for a typical choice of parameters of T and f.

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