Hypercyclic operators, Gauss measures and Polish dynamical systems

DOI10.1007/s11856-015-1194-4zbMath1339.47011arXiv1211.0105OpenAlexW2263082725MaRDI QIDQ891075

Yiftach Dayan, Shmuel Glasner

Publication date: 16 November 2015

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

Full work available at URL: https://arxiv.org/abs/1211.0105

zbMATH Keywords

Gaussian measurehypercyclic operatorsfrequently hypercyclic operatorsPolish dynamical systemssyndetically transitive systems

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Cyclic vectors, hypercyclic and chaotic operators (47A16)

Related Items (2)

Linear dynamical systems on Hilbert spaces: typical properties and explicit examples ⋮ Orbital and spectral aspects of hypercyclic operators and semigroups

Cites Work

• Mixing operators and small subsets of the circle
• Hilbertian Jamison sequences and rigid dynamical systems
• Unimodular eigenvalues, uniformly distributed sequences and linear dynamics
• Substitution dynamical systems - spectral analysis
• Frequently dense orbits
• A new class of frequently hypercyclic operators
• Invariant Gaussian measures for operators on Banach spaces and linear dynamics
• On the spectrum of frequently hypercyclic operators
• Sensitive dependence on initial conditions
• Gaussian Hilbert Spaces
• Locally equicontinuous dynamical systems
• Non-recurrence sets for weakly mixing linear dynamical systems
• Residual properties and almost equicontinuity.
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