Journal of the
Korean Mathematical Society JKMS

Anosov families were introduced by A. Fisher and P. Arnoux motivated by generalizing the notion of Anosov diffeomorphism defined on a compact Riemannian manifold. Roughly, an Anosov family is a two-sided sequence of diffeomorphisms (or non-stationary dynamical system) with similar behavior to an Anosov diffeomorphisms. We show that the set consisting of Anosov families is an open subset of the set consisting of two-sided sequences of diffeomorphisms, which is equipped with the strong topology (or Whitney topology).

Keywords: Anosov families, Anosov diffeomorphism, random dynamical systems, non-stationary dynamical systems, non-autonomous dynamical systems

MSC numbers: 37D20, 37C75, 37B55