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Surjunctivity and topological rigidity of algebraic dynamical systems

Published online by Cambridge University Press:  20 June 2017

SIDDHARTHA BHATTACHARYA ,
TULLIO CECCHERINI-SILBERSTEIN  and
MICHEL COORNAERT
SIDDHARTHA BHATTACHARYA
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Mumbai 400005, India email siddhart@math.tifr.res.in
TULLIO CECCHERINI-SILBERSTEIN
Affiliation:
Dipartimento di Ingegneria, Università del Sannio, C.so Garibaldi 107, 82100 Benevento, Italy email tullio.cs@sbai.uniroma1.it
MICHEL COORNAERT
Affiliation:
Université de Strasbourg, CNRS, IRMA UMR 7501, F-67000 Strasbourg, France email michel.coornaert@math.unistra.fr
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Abstract

Let $X$ be a compact metrizable group and let $\unicode[STIX]{x1D6E4}$ be a countable group acting on $X$ by continuous group automorphisms. We give sufficient conditions under which the dynamical system $(X,\unicode[STIX]{x1D6E4})$ is surjunctive, i.e. every injective continuous map $\unicode[STIX]{x1D70F}:X\rightarrow X$ commuting with the action of $\unicode[STIX]{x1D6E4}$ is surjective.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 3 , March 2019 , pp. 604 - 619
Copyright
© Cambridge University Press, 2017 

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