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Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 4, Pages 801–834 (Mi izv1536)  

This article is cited in 18 scientific papers (total in 18 papers)

Spectral properties of generic dynamical systems

A. M. Stepin

Abstract: Dynamical systems with new spectral properties are constructed using approximation theory. It is proved that these properties are generic (in a metric and topological sense) and realized within the class of smooth systems preserving a smooth measure.
Bibliography: 21 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 29:1, 159–192

Bibliographic databases:

UDC: 517.987
MSC: Primary 28D05, 47A35; Secondary 28D20, 54H20, 58F11
Received: 29.11.1984

Citation: A. M. Stepin, “Spectral properties of generic dynamical systems”, Izv. Akad. Nauk SSSR Ser. Mat., 50:4 (1986), 801–834; Math. USSR-Izv., 29:1 (1987), 159–192

Citation in format AMSBIB
\by A.~M.~Stepin
\paper Spectral properties of generic dynamical systems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1986
\vol 50
\issue 4
\pages 801--834
\jour Math. USSR-Izv.
\yr 1987
\vol 29
\issue 1
\pages 159--192

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    1. V. V. Ryzhikov, “Joinings and Multiple Mixing of Finite Rank Actions”, Funct. Anal. Appl., 27:2 (1993), 128–140  mathnet  crossref  mathscinet  zmath  isi
    2. V. V. Ryzhikov, “The isomorphism of measure-preserving transformations with isomorphic Cartesian powers is typical”, Math. Notes, 59:4 (1996), 453–456  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. V. Ryzhikov, “Intertwinings of tensor products, and the stochastic centralizer of dynamical systems”, Sb. Math., 188:2 (1997), 237–263  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. V. V. Ryzhikov, “On the Ranks of an Ergodic Automorphism $T\times T$”, Funct. Anal. Appl., 35:2 (2001), 151–153  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. S. V. Tikhonov, “O svyazi metricheskikh i spektralnykh svoistv $\mathbb{Z}^{d}$-deistvii”, Fundament. i prikl. matem., 8:4 (2002), 1179–1192  mathnet  mathscinet  zmath  elib
    6. V. V. Ryzhikov, “Partial Multiple Mixing on Subsequences May Distinguish between Automorphisms $T$ and $T^{-1}$”, Math. Notes, 74:6 (2003), 841–847  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. V. V. Ryzhikov, A. E. Troitskaya, “Tensor roots of isomorphisms and weak limits of transformations”, Math. Notes, 80:4 (2006), 563–566  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. V. V. Ryzhikov, “Weak limits of powers, simple spectrum of symmetric products, and rank-one mixing constructions”, Sb. Math., 198:5 (2007), 733–754  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. S. V. Tikhonov, “A complete metric in the set of mixing transformations”, Sb. Math., 198:4 (2007), 575–596  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    10. A. E. Troitskaya, “On isomorphity of measure-preserving $\mathbb Z^2$-actions that have isomorphic Cartesian powers”, J. Math. Sci., 159:6 (2009), 879–893  mathnet  crossref  mathscinet  zmath  elib  elib
    11. V. V. Ryzhikov, “Spectral multiplicities and asymptotic operator properties of actions with invariant measure”, Sb. Math., 200:12 (2009), 1833–1845  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. A. I. Danilenko, V. V. Ryzhikov, “Spectral Multiplicities of Infinite Measure Preserving Transformations”, Funct. Anal. Appl., 44:3 (2010), 161–170  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. ALEXANDRE I. DANILENKO, “A survey on spectral multiplicities of ergodic actions”, Ergod. Th. Dynam. Sys, 2011, 1  crossref
    14. V. V. Ryzhikov, “Simple spectrum of the tensor product of powers of a mixing automorphism”, Trans. Moscow Math. Soc., 73 (2012), 183–191  mathnet  crossref  mathscinet  zmath  elib
    15. R. A. Konev, V. V. Ryzhikov, “On the Collection of Spectral Multiplicities $\{2,4,…,2^n\}$ for Totally Ergodic $\mathbb{Z}^2$-Actions”, Math. Notes, 96:3 (2014), 360–368  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    16. A. Yu. Kushnir, V. V. Ryzhikov, “Weak Closures of Ergodic Actions”, Math. Notes, 101:2 (2017), 277–283  mathnet  crossref  crossref  mathscinet  isi  elib
    17. V. V. Ryzhikov, A. E. Troitskaya, “Peremeshivayuschie potoki s odnorodnym spektrom kratnosti 2”, Fundament. i prikl. matem., 21:5 (2016), 191–197  mathnet
    18. M. S. Lobanov, V. V. Ryzhikov, “Special weak limits and simple spectrum of the tensor products of flows”, Sb. Math., 209:5 (2018), 660–671  mathnet  crossref  crossref  adsnasa  isi  elib
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