Ergodic Theory and Dynamical Systems



Finite entropy characterizes topological rigidity on connected groups


SIDDHARTHA BHATTACHARYA a1 and THOMAS WARD a2
a1 School of Mathematics, Tata Institute of Fundamental Research, Bombay 400005, India (e-mail: siddhart@math.tifr.res.in)
a2 School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK (e-mail: t.ward@uea.ac.uk)

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

Abstract

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)