Weak forms of topological and measure-theoretical equicontinuity: relationships with discrete spectrum and sequence entropy

DOI10.1017/etds.2015.83zbMath1366.37019arXiv1402.7327OpenAlexW2963451602MaRDI QIDQ2989981

Felipe García-Ramos

Publication date: 9 June 2017

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.7327

zbMATH Keywords

ergodic measuremeasure-theoretical sensitivity

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Topological entropy (37B40) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Forward mean proximal pairs and zero entropy
• Measure-theoretical sensitivity and equicontinuity
• Mean-L-stable systems
• Combinatorial independence in measurable dynamics
• Interval maps, factors of maps, and chaos
• Pointwise theorems for amenable groups.
• Sequence entropy pairs and complexity pairs for a measure.
• Measures and probabilities
• Independence in topological and \(C^*\)-dynamics
• Ergodic transformation groups with a pure point spectrum
• On pairwise sensitivity
• Quasicrystals and almost periodicity
• Operator methods in classical mechanics. II
• Tame systems and scrambled pairs under an Abelian group action
• G -odometers and their almost one-to-one extensions
• Local entropy theory
• The Ergodic Theory of Lattice Subgroups (AM-172)
• Classes of linear automata
• Topological Sequence Entropy
• A disjointness theorem involving topological entropy
• Null systems and sequence entropy pairs
• Stronger forms of sensitivity for dynamical systems
• On tame dynamical systems
• Stability Properties of Flows with Pure Point Spectrum
• ON METRIC INVARIANTS OF ENTROPY TYPE
• Mean equicontinuity and mean sensitivity

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