Topologically mixing extensions of endomorphisms on Polish groups

John Burke; Leonardo Pinheiro

doi:10.4995/agt.2022.15187

Authors

John Burke Rhode Island College
Leonardo Pinheiro Rhode Island College https://orcid.org/0000-0002-1633-3606

DOI:

https://doi.org/10.4995/agt.2022.15187

Keywords:

weak mixing, Polish group, hypercyclicity criterion

Abstract

In this paper we study the dynamics of continuous endomorphisms on Polish groups. We offer necessary and sufficient conditions for a continuous endomorphism on a Polish group to be weakly mixing. We prove that any continuous endomorphism of an abelian Polish group can be extended in a natural way to a topologically mixing endomorphism on the countable infinite product of said group.

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Author Biographies

John Burke, Rhode Island College

Department of Mathematical Sciences

Leonardo Pinheiro, Rhode Island College

Associate Professor,

Department of Mathematical Sciences

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