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Sbornik: Mathematics, 2009, Volume 200, Issue 1, Pages 35–76
DOI: https://doi.org/10.1070/SM2009v200n01ABEH003986 (Mi sm4925) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Some properties of singular hyperbolic attractors

E. A. Sataev

Obninsk State Technical University for Nuclear Power Engineering
English version PDF (482 kB) Citations (11)
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DOI: https://doi.org/10.1070/SM2009v200n01ABEH003986
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.
Received: 21.03.2008
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 1, Pages 37–80
DOI: https://doi.org/10.4213/sm4925
Bibliographic databases:
UDC: 517.938
MSC: Primary 37D10; Secondary 34D45, 37C10, 37C75, 37D20, 37D30
Language: English
Original paper language: Russian
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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    • This publication is cited in the following 11 articles:
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    References:42
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