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Hypercyclic and mixing composition operators on $\mathscr{O}_M(\mathbb{R})$ (2310.09104v2)
Published 13 Oct 2023 in math.FA
Abstract: In this paper we characterize mixing composition operators acting on the space $\mathscr{O}_M(\mathbb{R})$ of slowly increasing smooth functions. Moreover we relate the mixing property of those operators with the solvability of Abel's functional equation and we give a sufficient condition for sequential hypercyclicity of composition operators on $\mathscr{O}_M(\mathbb{R})$. This is used to prove that many mixing composition operators are hypercyclic.