Geodesic
Stochastic properties of the singular hyperbolic attractors
Russian journal of nonlinear dynamics, Tome 6 (2010) no. 1, pp. 187-206

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In 1998 in paper of D. V. Turaev and L. P. Shilnikov there was introduced the definition of the pseudohyperbolic flow. The pseudohyperbolic flow is the flow such that in every point of the phase space there exists decomposition of the tangent bandle to sum of two spaces such that in one of these spaces there is expanding of volume. Independently in paper of C. Morales, M. J. Pacifico and E. Pujals was introduced the definition of the singular hyperbolic flow. Singular hyperbolic attractors satisfy more strong conditions then pseudohyperbolic ones. This paper is devoted to the theory of Sinai–Bowen–Ruelle measures for singular hyperbolic attractors. There are established such properties as ergodicity, mixing, continuous dependence of the invariant measures on flow.
Keywords: pseudohyperbolicity, singular hyperbolic system, invariant measure, ergodicity, mixing. 
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E. A. Sataev. Stochastic properties of the singular hyperbolic attractors. Russian journal of nonlinear dynamics, Tome 6 (2010) no. 1, pp. 187-206. http://geodesic.mathdoc.fr/item/ND_2010_6_1_a13/