On aperiodicity and hypercyclic weighted translation operators

Abstract

We give several equivalent characterization of aperiodicity of an element on locally compact group $G$, and give an intuition for "How strong does the aperiodicity of an element affect the existence of hypercyclic weighted translation operators?". In fact, if $a$ is an aperiodic element in $G$, then there exists a mixing, chaotic and frequently hypercyclic weighted translation $T_{a,w}$ on $L^p(G)$.

17 pages, no figures

References in corpus (1)

• Proper metrics on locally compact groups, and proper affine isometric actions on Banach spaces

Cited by in corpus (4)

• Linear dynamics of cosine operator functions on solid Banach function spaces
• Hypercyclic Operators on Hilbert C*-modules
• Dynamics of operators on the space of Radon measures
• Chaotic translations on weighted Orlicz spaces