Isomorphism rigidity of algebraic Z^d-actions

2001/08/06 by Siddhartha Bhattacharya, Bhattacharya, Siddhartha
Computer Science · Mathematics · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.DS #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0108033

10 pages

arxiv created 2001/08/06 · openalex publication_date 2001/08/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An algebraic Z^d-action is an action of Z^d on a compact abelian group X by automorphisms of X. We prove that for d ≥ 8, there exist mixing zero entropy algebraic Z^d-actions which do not exhibit isomorphism rigidity property.

Related

• Isomorphism rigidity of commuting automorphisms
• Isomorphism rigidity in entropy rank two
• Rigidity of measurable structure for Z^d-actions by automorphisms of a torus
• Rigidity of the measurable structure for algebraic actions of higher rank abelian groups
• Rigidity of multiparameter actions