On the ergodicity of infinite antisymmetric extensions of symmetric IETs

2023/04/04 by Berk, Przemysław, Trujillo, Frank
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.01868

Abstract

In this article, we consider skew product extensions over symmetric interval exchange transformations with respect to the cocycle f(x)=χ_(0,1/2)-χ_(1/2,1). More precisely, we prove that for almost every interval exchange transformation T with symmetric combinatorial data, the skew product T_f: [0, 1) × \mathbb Z → [0, 1) × \mathbb Z given by T_f(x,r)=(T(x),r+f(x)) is ergodic with respect to the product of the Lebesgue and counting measure.

Related

• Ergodic properties of infinite extension of symmetric interval exchange transformations
• Ergodicity of skew-products over typical IETs
• Ergodicity of skew products over linearly recurrent IETs
• On the ergodicity of anti-symmetric skew products with singularities and its applications
• Ergodicity of explicit logarithmic cocycles over IETs