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. 
@article{IM2_1976_10_6_a5,
     author = {Ya. B. Pesin},
     title = {Families of invariant manifolds corresponding to nonzero characteristic exponents},
     journal = {Izvestiya. Mathematics },
     pages = {1261--1305},
     publisher = {mathdoc},
     volume = {10},
     number = {6},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1976_10_6_a5/}
}
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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/