Bhattacharya, Siddhartha; Ward, Thomas Finite entropy characterizes topological rigidity on connected groups. (English) Zbl 1076.37004 Ergodic Theory Dyn. Syst. 25, No. 2, 365-373 (2005). 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. Cited in 5 Documents 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.) Keywords:algebraic \(\mathbb{Z}^d\)-actions; topological rigidity; topology entropy PDFBibTeX XMLCite \textit{S. Bhattacharya} and \textit{T. Ward}, Ergodic Theory Dyn. Syst. 25, No. 2, 365--373 (2005; Zbl 1076.37004) Full Text: DOI arXiv