# Disjointness of the convolutionsfor Chacon's automorphism

Colloquium Mathematicum (2000)

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

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topPrikhod'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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- [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- [5] A. B. Katok, Constructions in Ergodic Theory, unpublished lecture notes.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.

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