Topologically mixing extensions of endomorphisms on Polish groups

Authors

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

References

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Published

2022-04-01

How to Cite

[1]
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.

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Articles