The ergodicity of 1-Lipschitz transformations on 2-adic spheres

  • Ekaterina Yurova

    Linnaeus University, Vaxjo, Sweden
The ergodicity of 1-Lipschitz transformations on 2-adic spheres cover
Download Chapter PDF

A subscription is required to access this book chapter.

Abstract

In this paper we present results about ergodicity of dynamical systems on 22-adic spheres for 1-Lipschitz maps f:Z2Z2f:\mathbb Z_2\rightarrow \mathbb Z_2 announced in [8], and extension of Theorem 3 from [8] for the case of spheres of radii greater than 18.\frac{1}{8}. We propose a new approach to study ergodic properties of 1-Lipschitz transformations of 22-adic spheres. We use a representation of continuous functions ff via its van der Put series. This technique allows us to go beyond the classes of smooth 1-Lipschitz transformations which were studied earlier.