Some properties of singular hyperbolic attractors

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.
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