Geodesic
Families of invariant manifolds corresponding to nonzero characteristic exponents
Izvestiya. Mathematics, Tome 10 (1976) no. 6, pp. 1261-1305 
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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     author = {Ya. B. Pesin},
     title = {Families of invariant manifolds corresponding to nonzero characteristic exponents},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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[2] Anosov D. V., Sinai Ya. G., “Nekotorye gladkie ergodicheskie sistemy”, Uspekhi matem. nauk, 22:5 (1967), 107–168 | MR

[3] Brin M. I., Pesin Ya. B., “Chastichno giperbolicheskie dinamicheskie sistemy”, Izv. AN SSSR. Ser. matem., 38 (1974), 170–212 | MR | Zbl

[4] Bylov B. F., Vinograd R. E., Grobman D. M., Nemytskii V. V., Teoriya pokazatelei Lyapunova, Nauka, M., 1966 | Zbl

[5] Dedonne Zh., Osnovy sovremennogo analiza, Mir, M., 1964

[6] Hadamard J., “Sur l'itération et les solutions asymptotiques des équations différentielles”, Bull. Soc. Math. France, 29 (1901), 224–228 | Zbl

[7] Oseledets V. I., “Multiplikativnaya ergodicheskaya teorema. Kharakteristicheskie pokazateli Lyapunova dinamicheskikh sistem”, Tr. Mosk. matem. ob-va, 19 (1968), 179–210 | Zbl

[8] Perron O., “Die Stabilitätsfrage bei Difierentialgleichungen”, Math. Zs., 32 (1930), 703–728 | DOI | MR | Zbl

[9] Pesin Ya. B., “Kharakteristicheskie pokazateli Lyapunova i ergodicheskie svoistva gladkikh dinamicheskikh sistem s invariantnoi meroi”, Dokl. AN SSSR, 226:4 (1976), 774–777 | MR | Zbl

[10] Sternberg S., Lektsii po differentsialnoi geometrii, Mir, M., 1970 | MR | Zbl