Geodesic
Partially hyperbolic dynamical systems
Izvestiya. Mathematics , Tome 8 (1974) no. 1, pp. 177-218.

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Smooth dynamical systems having contracting and expanding invariant foliations (of not necessarily complementary dimensions) are investigated. Ergodicity and the $K$-property are established for such dynamical systems under additional assumptions. 
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M. I. Brin; Ya. B. Pesin. Partially hyperbolic dynamical systems. Izvestiya. Mathematics , Tome 8 (1974) no. 1, pp. 177-218. http://geodesic.mathdoc.fr/item/IM2_1974_8_1_a9/

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