Cyclic composition operators on separable locally compact metric spaces
It is proved 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, it is shown 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 the circle are discussed. This study is motivated by results of \textit{Z. Yin} [Int. J. Bifurcation Chaos Appl. Sci. Eng. 27, No. 6, Article ID 1750084, 12 p. (2017; Zbl 1370.37074)] who implicitly asked if the no-fixed-point condition is necessary for a composition operator to be cyclic on the real line.
scientific article; zbMATH DE number 7047512
scientific article