On the genericity of the shadowing property for conservative homeomorphisms

DOI10.1090/proc/13526zbMath1402.37011arXiv1606.02924OpenAlexW2962824392MaRDI QIDQ3177836

Pierre-Antoine Guihéneuf, Thibault Lefeuvre

Publication date: 2 August 2018

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.02924

zbMATH Keywords

shadowing propertyperiodic shadowing propertyconservative homeomorphism

Mathematics Subject Classification ID

Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (14)

On -genericity of distributional chaos ⋮ The equivalent condition of \(G\)-asymptotic tracking property and \(G\)-Lipschitz tracking property ⋮ The \(G\)-sequence shadowing property and \(G\)-equicontinuity of the inverse limit spaces under group action ⋮ Stability of the rotation set of area-preserving toral homeomorphisms ⋮ Realization of rotation vectors for volume preserving homeomorphisms of the torus ⋮ S-limit shadowing is generic for continuous Lebesgue measure-preserving circle maps ⋮ Dynamical property of the shift map under group action ⋮ Transitively-saturated property, Banach recurrence and Lyapunov regularity ⋮ Typical properties of interval maps preserving the Lebesgue measure ^* ⋮ Intermediate Lyapunov exponents for systems with periodic orbit gluing property ⋮ On the rotation sets of generic homeomorphisms on the torus ⋮ Topological aspects of incompressible flows ⋮ The rotation sets of most volume preserving homeomorphisms on \(\mathbb{T}^d\) are stable, convex and rational polyhedrons ⋮ Periodic points and shadowing for generic Lebesgue measure-preserving interval maps

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