Disjointness of the convolutionsfor Chacon's automorphism

A. Prikhod'ko; V. Ryzhikov

Colloquium Mathematicum (2000)

  • Volume: 84/85, Issue: 1, page 67-74
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Prikhod'ko, A., and Ryzhikov, V.. "Disjointness of the convolutionsfor Chacon's automorphism." Colloquium Mathematicum 84/85.1 (2000): 67-74. <http://eudml.org/doc/210809>.

@article{Prikhodko2000,
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 $σ^\{*d\} ⊥ σ^\{*d^\{\prime \}\}$. 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.},
author = {Prikhod'ko, A., Ryzhikov, V.},
journal = {Colloquium Mathematicum},
keywords = {ergodic automorphism; maximal spectral type; Chacon's automorphism},
language = {eng},
number = {1},
pages = {67-74},
title = {Disjointness of the convolutionsfor Chacon's automorphism},
url = {http://eudml.org/doc/210809},
volume = {84/85},
year = {2000},
}

TY - JOUR
AU - Prikhod'ko, A.
AU - Ryzhikov, V.
TI - Disjointness of the convolutionsfor Chacon's automorphism
JO - Colloquium Mathematicum
PY - 2000
VL - 84/85
IS - 1
SP - 67
EP - 74
AB - 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 $σ^{*d} ⊥ σ^{*d^{\prime }}$. 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.
LA - eng
KW - ergodic automorphism; maximal spectral type; Chacon's automorphism
UR - http://eudml.org/doc/210809
ER -

References

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  1. [1] S. Ferenczi, Systems of finite rank, Colloq. Math. 73 (1997), 35-65. 
  2. [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. [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. [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. [5] A. B. Katok, Constructions in Ergodic Theory, unpublished lecture notes. 
  6. [6] O V. I. Oseledec, An automorphism with simple and continuous spectrum not having the group property, Math. Notes 5 (1969), 196-198. 
  7. [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. [8] A. M. Stepin, Spectral properties of generic dynamical systems, Math. USSR-Izv. 29 (1987), 159-192. 

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