Orbital shadowing and stability for vector fields

DOI10.1016/j.jde.2020.01.026zbMath1441.37033OpenAlexW3004240069MaRDI QIDQ1989439

Ming Li

Publication date: 22 April 2020

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2020.01.026

zbMATH Keywords

structural stabilityvector fieldorbital shadowing\( \Omega \)-stability

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Stability theory for smooth dynamical systems (37C75)

Related Items (1)

Oriented and orbital shadowing for vector fields

Cites Work

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• On the singular-hyperbolicity of star flows
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• Stability theorems and hyperbolicity in dynamical systems
• Pseudo-orbit tracing property and strong transversality of diffeomorphisms on closed manifolds
• Shadowing in structurally stable flows
• Shadowing in dynamical systems
• Orbital and weak shadowing properties
• Vector fields with the oriented shadowing property
• Nonsingular star flows satisfy Axiom A and the no-cycle condition
• Extended f-orbits are approximated by orbits
• 𝐶¹ Connecting Lemmas
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• Invariant manifolds

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