Vector fields with the oriented shadowing property

DOI10.1016/J.JDE.2009.09.024zbMath1190.37019arXiv1010.3308OpenAlexW2011449610MaRDI QIDQ2379270

Sergei Yu. Pilyugin, Sergey B. Tikhomirov

Publication date: 19 March 2010

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

Full work available at URL: https://arxiv.org/abs/1010.3308

zbMATH Keywords

structural stabilityvector fieldsoriented shadowing

Mathematics Subject Classification ID

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

Related Items (13)

Robustly shadowable chain transitive sets and hyperbolicity ⋮ Weakly shadowable vector fields on non-oriented surfaces ⋮ Oriented and orbital shadowing for vector fields ⋮ Asymptotic average shadowing property and chain transitivity for multiple flow systems ⋮ On shadowing system generated by a uniformly convergent mappings sequence ⋮ Theory of pseudo-orbit shadowing in dynamical systems ⋮ Weak shadowing property for flows on oriented surfaces ⋮ Lipschitz shadowing and structural stability of flows ⋮ Orbital shadowing and stability for vector fields ⋮ Orbital shadowing for 3-flows ⋮ An example of a vector field with the oriented shadowing property ⋮ Oriented shadowing property and \(\Omega\)-stability for vector fields ⋮ Periodic shadowing of vector fields

Cites Work

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• 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
• \(C^{0}\) transversality and shadowing properties
• Nonsingular star flows satisfy Axiom A and the no-cycle condition
• The \(\Omega\)-stability theorem for flows
• Vector fields with topological stability
• The C¹ Closing Lemma, including Hamiltonians
• Stability Properties of One-Parameter Flows

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