Download PDF - Disjointness of the convolutionsfor Chacon's automorphismAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Disjointness of the convolutionsfor Chacon's automorphism

Authors 1, 1

Affiliations

  1. Department of Mathematics, Moscow State University, 119899 Moscow, Russia

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.

Bibliography

  1. S. Ferenczi, Systems of finite rank, Colloq. Math. 73 (1997), 35-65.
  2. G. Goodson, A survey of recent results in the spectral theory of ergodic dynamical systems, J. Dynam. Control Systems 5 (1999), 173-226.
  3. A. del Junco and M. Lemańczyk, Generic spectral properties of measure preserving maps and applications, Proc. Amer. Math. Soc., 115 (1992), 725-736.
  4. A. del Junco, A. M. Rahe and L. Swanson, Chacon's automorphism has minimal self-joinings, J. Anal. Math. 37 (1980), 276-284.
  5. A. B. Katok, Constructions in Ergodic Theory, unpublished lecture notes.
  6. O V. I. Oseledec, An automorphism with simple and continuous spectrum not having the group property, Math. Notes 5 (1969), 196-198.
  7. A. M. Stepin, On properties of spectra of ergodic dynamical systems with locally compact time, Dokl. Akad. Nauk SSR 169 (1966), 773-776 (in Russian).
  8. A. M. Stepin, Spectral properties of generic dynamical systems, Math. USSR-Izv. 29 (1987), 159-192.
Colloquium Mathematicum
2000/84/85/1
Export to PBN, Opens in new tab
Pages:
67-74
Main language of publication
English
Received
1999-05-10
Accepted
2000-02-11
Published
2000
Exact and natural sciences