Disjointness of the convolutionsfor Chacon's automorphism

Czasopismo

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• Autorzy: Prikhod'ko A. A. , Ryzhikov V. V.
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: ---
• Rocznik: 2000
• Tom: 84/85
• Numer: 1
• Strony: 67-74

Daty

wydano

2000

otrzymano

1999-05-10

poprawiono

2000-02-11

Twórcy

autor

Prikhod'ko A. A.

• Department of Mathematics, Moscow State University, 119899 Moscow, Russia

autor

Ryzhikov V. V.

• Department of Mathematics, Moscow State University, 119899 Moscow, Russia

Bibliografia

• [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• [5] A. B. Katok, Constructions in Ergodic Theory, unpublished lecture notes.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.