Local stable and unstable manifolds for Anosov families. (English) Zbl 1437.37038
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.
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.
Reviewer: Miguel Paternain (Montevideo)
MSC:
37D10 | Invariant manifold theory for dynamical systems |
37D20 | Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) |
37C60 | Nonautonomous smooth dynamical systems |
37H10 | Generation, random and stochastic difference and differential equations |