\(C^1\)-stably weakly shadowing homoclinic classes admit dominated splittings

DOI10.3934/DCDS.2010.27.205zbMath1195.37011OpenAlexW2093194459MaRDI QIDQ968743

Shaobo Gan, Kazuhiro Sakai, Lan Wen

Publication date: 6 May 2010

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

Full work available at URL: https://doi.org/10.3934/dcds.2010.27.205

zbMATH Keywords

pseudo-orbitshadowingdominated splittinghomoclinic classchain recurrent setpartially hyperbolicchain componentweak shadowing

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) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Notions of recurrence and recurrent behavior in topological dynamical systems (37B20)

Related Items (6)

Diffeomorphisms with \(C^1\)-stably average shadowing ⋮ Unnamed Item ⋮ Stably asymptotic average shadowing property and dominated splitting ⋮ Stable weakly shadowable volume-preserving systems are volume-hyperbolic ⋮ Stably weakly shadowing transitive sets and dominated splittings ⋮ Shadowable chain transitive sets

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