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Mat. Sb. (N.S.), 1988, Volume 136(178), Number 3(7), Pages 307–319 (Mi msb1743)  

This article is cited in 15 scientific papers (total in 15 papers)

Dynamical systems with an even-mulriplicity Lebesgue component in the spectrum

O. N. Ageev

Abstract: A general construction of ergodic transformations with Lebesgue component of finite multiplicity is proposed. All known examples with this property can be encompassed within the proposed construction. The spectral and combinatorial properties of the transformations are studied. It is shown that the construction permits one to obtain a continuum of spectrally nonisomorphic transformations with even-multiplicity Lebesgue component. As a rule, the transformations have a continuous spectrum. It is proved that continuum many metrically nonisomorphic transformations having the same spectrum are contained in the proposed class. Proof of all the results uses a combinatorial and approximation technique.
Figures: 4.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Sbornik, 1989, 64:2, 305–317

Bibliographic databases:

UDC: 517.987.5
MSC: 28D05
Received: 27.01.1987

Citation: O. N. Ageev, “Dynamical systems with an even-mulriplicity Lebesgue component in the spectrum”, Mat. Sb. (N.S.), 136(178):3(7) (1988), 307–319; Math. USSR-Sb., 64:2 (1989), 305–317

Citation in format AMSBIB
\by O.~N.~Ageev
\paper Dynamical systems with an even-mulriplicity Lebesgue component in the spectrum
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 136(178)
\issue 3(7)
\pages 307--319
\jour Math. USSR-Sb.
\yr 1989
\vol 64
\issue 2
\pages 305--317

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    This publication is cited in the following articles:
    1. Ferenczi S., Kwiatkowski J., “Rank and Spectral Multiplicity”, Studia Math., 102:2 (1992), 121–144  mathscinet  zmath  isi
    2. Goodson G., Kwiatkowski J., Lemanczyk M., Liardet P., “On the Multiplicity Function of Ergodic Group Extensions of Rotations”, Studia Math., 102:2 (1992), 157–174  mathscinet  zmath  isi
    3. O. N. Ageev, “Mixing in the components and rearrangements of $T_{\alpha,\beta}$”, Russian Math. Surveys, 49:2 (1994), 141–142  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. Kwiatkowski J., Lemanczyk M., “On the Multiplicity Function of Ergodic Group Extensions .2.”, Studia Math., 116:3 (1995), 207–215  mathscinet  zmath  isi
    5. Fraczek K., “Cyclic Space Isomorphism of Unitary Operators”, Studia Math., 124:3 (1997), 259–267  mathscinet  zmath  isi
    6. Filipowicz I., “Product Zeta(D)-Actions on a Lebesgue Space and their Applications”, Studia Math., 122:3 (1997), 289–298  mathscinet  zmath  isi
    7. O. N. Ageev, “The spectral multiplicity function and geometric representations of interval exchange transformations”, Sb. Math., 190:1 (1999), 1–28  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. Oleg Ageev, “The homogeneous spectrum problem in ergodic theory”, Invent math, 160:2 (2005), 417  crossref  mathscinet  zmath  isi  elib
    9. O. N. Ageev, “Nonsingular α-rigid maps”, J Dyn Control Syst, 2009  crossref  isi
    10. E. H. Abdalaoui, “On the spectrum of α-rigid maps”, J Dyn Control Syst, 2009  crossref  isi
    11. E. H. El Abdalaoui, M. Lemańczyk, “Approximate transitivity property and Lebesgue spectrum”, Mh Math, 2010  crossref
    12. E. H. Abdalaoui, M. Lemańczyk, “Approximately transitive dynamical systems and simple spectrum”, Arch. Math, 2011  crossref
    13. ALEXANDRE I. DANILENKO, “A survey on spectral multiplicities of ergodic actions”, Ergod. Th. Dynam. Sys, 2011, 1  crossref
    14. V. V. Ryzhikov, “Spectral multiplicity for powers of weakly mixing automorphisms”, Sb. Math., 203:7 (2012), 1065–1076  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    15. E. H. EL ABDALAOUI, M. G. NADKARNI, “A non-singular transformation whose spectrum has Lebesgue component of multiplicity one”, Ergod. Th. Dynam. Sys, 2014, 1  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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