Hypercyclic and topologically transitive semigroups of composition operators

摘要

We study the dynamical properties of semigroups of composition operators of continuous functions on a separable locally compact metric space X. In particular, we show that if E is a normed vector space and φ : X → X is one-to-one and runaway on X, then the composition operator f → φ o f on C(X, E) is topologically transitive and hypercyclic, where C(X, E) is the space of continuous functions from X into E with the compact-open topology.