Ultrafilters and Ramsey-type shadowing phenomena in topological dynamics

DOI10.1007/S11856-018-1739-4zbMath1416.37011OpenAlexW2884255670MaRDI QIDQ1617914

Piotr Oprocha, William Rea Brian

Publication date: 13 November 2018

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

Full work available at URL: https://doi.org/10.1007/s11856-018-1739-4

zbMATH Keywords

ultrafiltersyndetic setRamsey shadowing property

Mathematics Subject Classification ID

Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (5)

Shadowing, internal chain transitivity and \(\alpha \)-limit sets ⋮ Expansivity and unique shadowing ⋮ Preservation of shadowing in discrete dynamical systems ⋮ When is the beginning the end? On full trajectories, limit sets and internal chain transitivity ⋮ Orbital shadowing, \(\omega\)-limit sets and minimality

Cites Work

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• Dynamics of spacing shifts
• Dynamics in one dimension
• Algebra in the Stone-Čech compactification: theory and applications
• Ramsey Shadowing and minimal points
• Shadowing, thick sets and the Ramsey property
• Chain transitivity and variations of the shadowing property
• The topological dynamics of Ellis actions
• Divisible Properties and the Stone-Čech Compactification
• A characterization ofω-limit sets in shift spaces
• The -limit sets of quadratic Julia sets
• Shadowing and -limit sets of circular Julia sets

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