Topologically mixing extensions of endomorphisms on Polish groups




weak mixing, Polish group, hypercyclicity criterion


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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How to Cite

J. Burke and L. Pinheiro, “Topologically mixing extensions of endomorphisms on Polish groups”, Appl. Gen. Topol., vol. 23, no. 1, pp. 179–187, Apr. 2022.