Cyclic composition operators on separable locally compact metric spaces

摘要

We show that if a homeomorphism of a separable locally compact metric space has a unique fixed point that is attracting or repelling, then its corresponding composition operator is cyclic. On the real line, we show that a composition operator is cyclic if and only if its symbol has at most one fixed point. Other results on the real line and circle are also discussed. (C) 2019 Elsevier B.V. All rights reserved.