An Anosov family is a time-dependent sequence of diffeomorphisms \(f_i : M_i \rightarrow M_{i+1}\) having a hyperbolic behavior and defined on a sequence of compact Riemannian manifolds \(M_i\) for \(i\in \mathbb{Z}\). These families were introduced by P. Arnoux and A. M. Fisher [Ergodic Theory Dyn. Syst. 25, No. 3, 661–709 (2005; Zbl 1140.37314)] and generalize the notion of Anosov diffeomorphism defined on a compact Riemannian manifold.
In the present paper the author shows a generalized version of the Hadamard-Perron theorem. Local stable and unstable manifolds for Anosov families are also obtained.