Dynamics of composition operators on function spaces defined by local and global properties

TL;DR

This paper investigates the behavior of composition operators on locally convex function spaces over the real line, focusing on properties like supercyclicity, power boundedness, and ergodicity.

Contribution

It provides new results on the dynamics of composition operators, including conditions for supercyclicity and mean ergodicity in these function spaces.

Findings

Characterization of supercyclicity conditions

Results on power boundedness of operators

Convergence criteria for operator iterates

Abstract

In this paper we consider composition operators on locally convex spaces of functions defined on $\mathbb{R}$. We prove results concerning supercyclicity, power boundedness, mean ergodicity and convergence of the iterates in the strong operator topology.