Transitivity of composition operators induced by dynamics on locally compact spaces

Abstract: This paper investigates the transitivity of composition operators 𝑇𝜑𝑓 = 𝑓◦𝜑 on weightedcontinuous and 𝐿𝑝 spaces over locally compact spaces. Using the framework of Furstenberg families, we characterize different forms of operator transitivity (e.g.,-transitivity) via hittingtime sets, revealing a direct connection with the recurrence properties of the underlying map 𝜑. We show that weaker recurrence of 𝜑 corresponds to stronger transitivity of 𝑇𝜑. As applications, we prove that functions on compact subsets can be densely approximated by operator orbits, and that transitive subspaces exist even when the operator itself is not transitive.