Chain components with stably limit shadowing property are hyperbolic

DOI10.1186/1687-1847-2014-104zbMath1417.37108OpenAlexW2132903272WikidataQ59322608 ScholiaQ59322608MaRDI QIDQ1720221

Manseob Lee, Junmi Park

Publication date: 8 February 2019

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2014-104

zbMATH Keywords

hyperbolicshadowinghomoclinic classlimit shadowingchain component

Mathematics Subject Classification ID

Perturbations of ordinary differential equations (34D10) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50)

Related Items (5)

Eventual shadowing for chain transitive sets of $C^1$ generic dynamical systems ⋮ \(C^2\)-stably limit shadowing diffeomorphisms ⋮ Rough dependence upon initial data exemplified by explicit solutions and the effect of viscosity ⋮ Unnamed Item ⋮ CHAIN COMPONENTS WITH THE STABLE SHADOWING PROPERTY FOR C¹ VECTOR FIELDS

Cites Work

• Unnamed Item
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• \( C^1\)-stable shadowing diffeomorphisms
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• Pseudo-orbit tracing property and strong transversality of diffeomorphisms on closed manifolds
• Shadowing in dynamical systems
• An ergodic closing lemma
• \(C^1\)-stably shadowable chain components are hyperbolic
• Hyperbolicity and types of shadowing for \(C^1\) generic vector fields
• Sets of dynamical systems with various limit shadowing properties
• Diffeomorphisms satisfying the specification property
• C¹-stably shadowable chain components
• On almost specification and average shadowing properties
• Necessary Conditions for Stability of Diffeomorphisms
• Hyperbolic sets with the strong limit shadowing property

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