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Surjunctivity and topological rigidity of algebraic dynamical systems



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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Surjunctivity and topological rigidity of algebraic dynamical systems



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