Geodesic
Some properties of singular hyperbolic attractors
Sbornik. Mathematics, Tome 200 (2009) no. 1, pp. 35-76

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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. 
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E. A. Sataev. Some properties of singular hyperbolic attractors. Sbornik. Mathematics, Tome 200 (2009) no. 1, pp. 35-76. http://geodesic.mathdoc.fr/item/SM_2009_200_1_a1/