2020/11/21 by Abbar, Arafat, Coine, Clément, Petitjean, Colin
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2011.10800
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 \widehatf : \mathcal F(M) → \mathcal 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 \widehatf : \mathcal F(M) → \mathcal 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.