On the Dynamics of Lipschitz Operators
Résumé
By the linearization property of Lipschitz-free spaces, any Lipschitz map f : M → N between two pointed metric spaces may be extended uniquely to a bounded linear operator f : F (M) → F (N) between their corresponding Lipschitz-free spaces. In this note, we explore the connections between the dynamics of Lipschitz self-maps f : M → M and the linear dynamics of their extensions f : F (M) → F (M). This not only allows us to relate topological dynamical systems to linear dynamical systems but also provide a new class of hypercyclic operators acting on Lipschitz-free spaces.
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