\( C^1\)-stable shadowing diffeomorphisms

DOI10.3934/DCDS.2008.22.683zbMath1153.37316OpenAlexW2066290193MaRDI QIDQ953814

Kazumine Moriyasu, Kazuhiro Sakai, Keon-Hee Lee

Publication date: 6 November 2008

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2008.22.683

zbMATH Keywords

pseudo-orbitshadowinghomoclinic classaxiom Ahyperbolic setchain recurrent setchain component\(C^1\)-stable shadowing property

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Partially hyperbolic systems and dominated splittings (37D30) Stability theory for smooth dynamical systems (37C75) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (10)

C¹-stably ℒ_pshadowable homoclinic classes ⋮ New criteria for hyperbolicity based on periodic sets ⋮ Stably average shadowable homoclinic classes ⋮ Chain components with \(C^1\)-stably orbital shadowing ⋮ Unnamed Item ⋮ Chain components with stably limit shadowing property are hyperbolic ⋮ CHAIN COMPONENTS WITH THE STABLE SHADOWING PROPERTY FOR C¹ VECTOR FIELDS ⋮ Hyperbolicity, transitivity and the two-sided limit shadowing property ⋮ Shadowable chain transitive sets ⋮ Inverse pseudo orbit tracing property for robust diffeomorphisms

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