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Finite entropy characterizes topological rigidity on connected groups

Published online by Cambridge University Press:  02 February 2005

SIDDHARTHA BHATTACHARYA  and
THOMAS WARD
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)
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Abstract

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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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 2 , April 2005 , pp. 365 - 373
Copyright
2005 Cambridge University Press