Structural stability and a characterization of Anosov families

TL;DR

This paper studies non-stationary hyperbolic dynamical systems called Anosov families, providing examples, invariant manifolds, stability results, and a characterization for specific classes.

Contribution

It introduces non-trivial examples of Anosov families and offers a new characterization along with stability and invariant manifold results.

Findings

Existence of invariant manifolds for Anosov families

Structural stability of certain Anosov families

Characterization of a specific class of Anosov families

Abstract

Anosov families are non-stationary dynamical systems with hyperbolic behavior. Non-trivial examples of Anosov families will be given in this paper. We show the existence of invariant manifolds, the structrural stability and a characterization for a certain class of Anosov families.