Families of Invariant Manifolds Corresponding to Nonzero Characteristic Exponents

A theorem on conditional stability is proved for a family of mappings of class C1 + , 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 Ljapunov characteristic exponent is nonzero. The property of absolute continuity is proved for these families.Bibliography: 10 titles.