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Finite entropy characterizes topological rigidity on connected groups. (English) Zbl 1076.37004

Summary: Let \(X_1\), \(X_2\) 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.

MSC:

37A15 General groups of measure-preserving transformations and dynamical systems
37B40 Topological entropy
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
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