Ergodic Theory and Dynamical Systems

Finite entropy characterizes topological rigidity on connected groups

a1 School of Mathematics, Tata Institute of Fundamental Research, Bombay 400005, India (e-mail:
a2 School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK (e-mail:

Article author query
bhattacharya s   [Google Scholar] 
ward t   [Google Scholar] 


Let $\mathsf{X}_1$, $\mathsf{X}_2$ be mixing connected algebraic dynamical systems with the descending chain condition. We show that every equivariant continuous map $\mathsf{X}_1\to\mathsf{X}_2$ is affine (that is, $\mathsf{X}_2$ is topologically rigid) if and only if the system $\mathsf{X}_2$ has finite topological entropy.

(Received February 3 2003)
(Revised January 17 2004)