Geodesic
Families of invariant manifolds corresponding to nonzero characteristic exponents
Izvestiya. Mathematics , Tome 10 (1976) no. 6, pp. 1261-1305.

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A theorem on conditional stability is proved for a family of mappings of class $C^{1+\varepsilon}$, satisfying a condition more general than Ljapunov regularity. Using this theorem, families of invariant manifolds are constructed for a diffeomorphism of a smooth manifold onto a set where at least one Lyapunov characteristic exponent is nonzero. The property of absolute continuity is proved for these families. Bibliography: 10 titles. 
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Ya. B. Pesin. Families of invariant manifolds corresponding to nonzero characteristic exponents. Izvestiya. Mathematics , Tome 10 (1976) no. 6, pp. 1261-1305. http://geodesic.mathdoc.fr/item/IM2_1976_10_6_a5/

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