Robustly chain transitive diffeomorphisms

DOI10.1186/s13660-015-0752-yzbMath1353.37059OpenAlexW1024853408WikidataQ59430590 ScholiaQ59430590MaRDI QIDQ264982

Manseob Lee

Publication date: 1 April 2016

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-015-0752-y

zbMATH Keywords

hyperbolicdominated splittingtransitivelocally maximal

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Partially hyperbolic systems and dominated splittings (37D30) Stability theory for smooth dynamical systems (37C75)

Related Items

Eventual shadowing for chain transitive sets of $C^1$ generic dynamical systems, \(C^2\)-stably limit shadowing diffeomorphisms, Local topological stability for diffeomorphisms, Lyapunov stable homoclinic classes for smooth vector fields, Unnamed Item, A type of the shadowing properties for generic view points, Asymptotic orbital shadowing property for diffeomorphisms

Cites Work

• Unnamed Item
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• A proof of the \(C^ 1\) stability conjecture
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• An ergodic closing lemma
• A structural stability theorem
• Flows with the (asymptotic) average shadowing property on three-dimensional closed manifolds
• Perturbations of the derivative along periodic orbits
• Diffeomorphisms in ℱ¹(M) satisfy Axiom A