Families of invariant manifolds corresponding to nonzero characteristic exponents

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.