Chain components with \(C^1\)-stably orbital shadowing

DOI10.1186/1687-1847-2013-67zbMath1380.37054OpenAlexW2104353564WikidataQ59293262 ScholiaQ59293262MaRDI QIDQ1693484

Manseob Lee

Publication date: 31 January 2018

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

Full work available at URL: https://doi.org/10.1186/1687-1847-2013-67

zbMATH Keywords

hyperbolicshadowinghomoclinic classorbital shadowingchain component

Mathematics Subject Classification ID

Generic properties, structural stability of dynamical systems (37C20) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (5)

Unnamed Item ⋮ Orbital shadowing property on chain transitive sets for generic diffeomorphisms ⋮ Unnamed Item ⋮ CHAIN COMPONENTS WITH THE STABLE SHADOWING PROPERTY FOR C¹ VECTOR FIELDS ⋮ Lyapunov-type inequalities for a class of fractional differential equations

Cites Work

• Unnamed Item
• \( C^1\)-stable shadowing diffeomorphisms
• Stability theorems and hyperbolicity in dynamical systems
• Pseudo-orbit tracing property and strong transversality of diffeomorphisms on closed manifolds
• Shadowing in dynamical systems
• An ergodic closing lemma
• Orbital and weak shadowing properties
• Bifurcation and chain recurrence
• C¹-stably shadowable chain components
• Diffeomorphisms in ℱ¹(M) satisfy Axiom A
• Homoclinic tangencies and dominated splittings
• Necessary Conditions for Stability of Diffeomorphisms

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