Ergodic homoclinic groups, Sidon constructions and Poisson suspensions

DOI10.1090/S0077-1554-2014-00227-2zbMath1316.28013MaRDI QIDQ5254445

V. V. Ryzhikov

Publication date: 9 June 2015

Published in: Transactions of the Moscow Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

singular spectrumSidon setmultiple mixingPoisson suspensionergodic actionshomoclinic transformationsrank-one construction

Mathematics Subject Classification ID

Measure-preserving transformations (28D05)

Related Items (8)

Group actions: Entropy, mixing, spectra, and generic properties ⋮ Special weak limits and simple spectrum of the tensor products of flows ⋮ Uniform convergence on subspaces in the von Neumann ergodic theorem with discrete time ⋮ On the centralizer of an infinite mixing rank-one transformation ⋮ Spectra of self-similar ergodic actions ⋮ Minimal self-joinings of infinite mixing actions of rank 1 ⋮ Weakly homoclinic groups of ergodic actions ⋮ Measure-preserving rank one transformations

Cites Work

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• Raghunathan's topological conjecture and distributions of unipotent flows
• A homoclinic version of the central limit theorem
• Generic mixing transformations are rank 1
• Approximation of mixing transformations
• Ergodic automorphisms with simple spectrum and rapidly decreasing correlations
• Mixing constructions with infinite invariant measure and spectral multiplicities
• Weak limits of powers, simple spectrum of symmetric products, and rank-one mixing constructions
• Poisson suspensions and infinite ergodic theory

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