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
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Abstract

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