Finite entropy characterizes topological rigidity

Mathematics – Dynamical Systems

Scientific paper

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11 pages, no figures

Scientific paper

10.1017/S0143385704000501

Let X_1 and X_2 be mixing connected algebraic dynamical systems with the
Descending Chain Condition. We show that every equivariant continuous map X_1
to X_2 is affine (that is, X_2 is topologically rigid) if and only if the
system X_2 has finite topological entropy.

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