Ergodicity of skew products over linearly recurrent IETs

2019/02/06 by Jon Chaika, Donald Robertson · 2 citations
Mathematics · Economics, Econometrics and Finance · #Mathematical Dynamics and Fractals #Economic theories and models #Functional Equations Stability Results

paper · doi:10.1112/jlms.12210

Abstract

We prove that the skew product over a linearly recurrent interval exchange transformation defined by almost any real-valued, mean-zero linear combination of characteristic functions of intervals is ergodic with respect to Lebesgue measure.

Citations

• Recurrence of Co-Cycles and Random Walks
• Ergodicity of cylinder flows arising from irregularities of distribution
• Non-ergodic ℤ -periodic billiards and infinite translation surfaces

Cited by

• Coexistence of two contrasting recurrence properties of certain non-integrable cocycles
• Ergodicity of explicit logarithmic cocycles over IETs

Related

• Ergodicity of skew-products over typical IETs
• Ergodic properties of infinite extension of symmetric interval exchange transformations
• On the ergodicity of infinite antisymmetric extensions of symmetric IETs
• Ergodic measures for periodic type ℤ^m-skew-products over Interval Exchange Transformations
• Skew-product systems over infinite interval exchange transformations