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Surjunctivity and topological rigidity of algebraic dynamical systems
Published online by Cambridge University Press: 20 June 2017
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.
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- © Cambridge University Press, 2017
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