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Finite entropy characterizes topological rigidity on connected groups

Published online by Cambridge University Press:  02 February 2005

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

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.

Type
Research Article
Copyright
2005 Cambridge University Press

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