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Mat. Sb., 2010, Volume 201, Number 3, Pages 107–160 (Mi msb7484)  

This article is cited in 4 scientific papers (total in 5 papers)

Invariant measures for singular hyperbolic attractors

E. A. Sataev

Obninsk State Technical University for Nuclear Power Engineering

Abstract: This paper continues the author's previous paper, where strong unstable spaces were constructed for a singular hyperbolic attractor. In this paper the existence of local strongly unstable manifolds and invariant measures of Sinaǐ-Bowen-Ruelle type is established. The properties of such measures are studied. It is proved that the number of ergodic components is finite and the set of periodic trajectories is dense.
Bibliography: 34 titles.

Keywords: singular hyperbolic systems, unstable manifolds, invariant measures, ergodicity.

DOI: https://doi.org/10.4213/sm7484

Full text: PDF file (808 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2010, 201:3, 419–470

Bibliographic databases:

UDC: 517.938
MSC: Primary 37D10; Secondary 37C10, 37C75, 37D20, 37D30, 34D45
Received: 10.11.2008 and 21.09.2009

Citation: E. A. Sataev, “Invariant measures for singular hyperbolic attractors”, Mat. Sb., 201:3 (2010), 107–160; Sb. Math., 201:3 (2010), 419–470

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. A. Sataev, “Stokhasticheskie svoistva singulyarno giperbolicheskikh attraktorov”, Nelineinaya dinam., 6:1 (2010), 187–206  mathnet  elib
    2. E. A. Sataev, “Mixing and eigenfunctions of singular hyperbolic attractors”, Sb. Math., 206:4 (2015), 572–599  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. S. M. Aseev, V. M. Buchstaber, R. I. Grigorchuk, V. Z. Grines, B. M. Gurevich, A. A. Davydov, A. Yu. Zhirov, E. V. Zhuzhoma, M. I. Zelikin, A. B. Katok, A. V. Klimenko, V. V. Kozlov, V. P. Leksin, M. I. Monastyrskii, A. I. Neishtadt, S. P. Novikov, E. A. Sataev, Ya. G. Sinai, A. M. Stepin, “Dmitrii Viktorovich Anosov (obituary)”, Russian Math. Surveys, 70:2 (2015), 369–381  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. Arbieto A., Lopez Barragan A.M., Morales Rojas C.A., “Homoclinic classes for sectional-hyperbolic sets”, Kyoto J. Math., 56:3 (2016), 531–538  crossref  mathscinet  zmath  isi  scopus
    5. Araujo V., Souza A., Trindade E., “Upper Large Deviations Bound For Singular-Hyperbolic Attracting Sets”, J. Dyn. Differ. Equ., 31:2 (2019), 601–652  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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