Finite entropy characterizes topological rigidity on connected groups

Siddhartha Bhattacharya; Thomas Ward

doi:10.1017/S0143385704000501

Finite entropy characterizes topological rigidity on connected groups

Siddhartha Bhattacharya, Thomas Ward

School of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

Let X1, X2 be mixing connected algebraic dynamical systems with the Descending Chain Condition. We show that every equivariant continuous map from X1 to X2 is affine (that is, X2 is topologically rigid) if and only if the system X2 has finite topological entropy.

Original language	English
Pages (from-to)	365-373
Number of pages	9
Journal	Ergodic Theory and Dynamical Systems
Volume	25
Issue number	2
DOIs	https://doi.org/10.1017/S0143385704000501
Publication status	Published - 2005

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10.1017/S0143385704000501

Cite this

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title = "Finite entropy characterizes topological rigidity on connected groups",

abstract = "Let X1, X2 be mixing connected algebraic dynamical systems with the Descending Chain Condition. We show that every equivariant continuous map from X1 to X2 is affine (that is, X2 is topologically rigid) if and only if the system X2 has finite topological entropy.",

author = "Siddhartha Bhattacharya and Thomas Ward",

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language = "English",

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AU - Ward, Thomas

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AB - Let X1, X2 be mixing connected algebraic dynamical systems with the Descending Chain Condition. We show that every equivariant continuous map from X1 to X2 is affine (that is, X2 is topologically rigid) if and only if the system X2 has finite topological entropy.

U2 - 10.1017/S0143385704000501

DO - 10.1017/S0143385704000501

M3 - Article

VL - 25

SP - 365

EP - 373

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

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ER -