Disjointness of the convolutionsfor Chacon's automorphism

Volume 84 / 2000

A. Prikhod'ko, V. Ryzhikov Colloquium Mathematicum 84 (2000), 67-74 DOI: 10.4064/cm-84/85-1-67-74

Abstract

The purpose of this paper is to show that if σ is the maximal spectral type of Chacon's transformation, then for any d ≠ d' we have $σ^{*d} ⊥ σ^{*d'}$. First, we establish the disjointness of convolutions of the maximal spectral type for the class of dynamical systems that satisfy a certain algebraic condition. Then we show that Chacon's automorphism belongs to this class.

Authors

  • A. Prikhod'ko
  • V. Ryzhikov

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