Homoclinic points and isomorphism rigidity of algebraic \(\mathbb Z^d\)-actions on zero-dimensional compact abelian groups

DOI10.1007/BF02785962zbMath1274.37016OpenAlexW1970478043MaRDI QIDQ2382233

Klaus Schmidt, Siddhartha Bhattacharya

Publication date: 28 September 2007

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02785962

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items (5)

Higher order mixing and rigidity of algebraic actions on compact abelian groups ⋮ Isomorphism rigidity in entropy rank two ⋮ Reversing and extended symmetries of shift spaces ⋮ Isomorphism rigidity of commuting automorphisms ⋮ 𝐶*-algebras of homoclinic and heteroclinic structure in expansive dynamics

Cites Work

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• A simple proof of the Bernoullicity of ergodic automorphisms on compact Abelian groups
• Zero-entropy algebraic \(\mathbb{Z}^d\)-actions that do not exhibit rigidity
• Isomorphism and measure rigidity for algebraic actions on zero-dimensional groups
• Rigidity of measurable structure for \(\mathbb Z^d\)-actions by automorphisms of a torus
• Almost block independence and Bernoullicity of \(\mathbb{Z}^ d\)-actions by automorphisms of compact Abelian groups
• Higher order mixing and rigidity of algebraic actions on compact abelian groups
• Homoclinic points of algebraic $\mathbb {Z}^d$-actions
• Expansive Subdynamics
• Dynamical systems of algebraic origin
• Isomorphism rigidity of irreducible algebraic \(\mathbb{Z}^d\)-actions

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