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Mat. Sb., 2009, Volume 200, Number 1, Pages 37–80 (Mi msb4925)  

This article is cited in 6 scientific papers (total in 6 papers)

Some properties of singular hyperbolic attractors

E. A. Sataev

Obninsk State Technical University for Nuclear Power Engineering

Abstract: The definition of a singular hyperbolic attractor was given in a paper by Morales, Pacifico, and Pujals in 1998. A similar definition was given by Turaev and Shil'nikov in 1998. This definition was motivated on the one hand by the well-known Lorenz model, and on the other hand by the definition of a hyperbolic attractor. We prove certain properties of singular hyperbolic attractors, which are subsequently used to prove the existence of invariant measures of Sinaĭ-Bowen-Ruelle type. The main result of the paper is a proof of the existence of an invariant family of strong unstable spaces on a sufficiently representative set.
Bibliography: 21 titles.

Keywords: singular hyperbolicity, stable manifolds, unstable spaces.

DOI: https://doi.org/10.4213/sm4925

Full text: PDF file (751 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:1, 35–76

Bibliographic databases:

UDC: 517.938
MSC: Primary 37D10; Secondary 34D45, 37C10, 37C75, 37D20, 37D30
Received: 21.03.2008

Citation: E. A. Sataev, “Some properties of singular hyperbolic attractors”, Mat. Sb., 200:1 (2009), 37–80; Sb. Math., 200:1 (2009), 35–76

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm4925
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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, “Invariant measures for singular hyperbolic attractors”, Sb. Math., 201:3 (2010), 419–470  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. Arbieto A., “Sectional Lyapunov exponents”, Proc. Amer. Math. Soc., 138:9 (2010), 3171–3178  crossref  mathscinet  zmath  isi
    3. E. A. Sataev, “Stokhasticheskie svoistva singulyarno giperbolicheskikh attraktorov”, Nelineinaya dinam., 6:1 (2010), 187–206  mathnet  elib
    4. 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
    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  mathscinet  zmath  isi
    6. Belykh V.N. Barabash N.V. Belykh I.V., “A Lorenz-Type Attractor in a Piecewise-Smooth System: Rigorous Results”, Chaos, 29:10 (2019), 103108  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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