HYPERBOLICITY OF HOMOCLINIC CLASSES OF VECTOR FIELDS

DOI10.1017/S1446788714000640zbMath1351.37102MaRDI QIDQ5253335

Seunghee Lee, Manseob Lee, Keon-Hee Lee

Publication date: 5 June 2015

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

homoclinic classhyperbolic closed orbitshadowablepersistently expansive

Mathematics Subject Classification ID

Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Dynamical systems with hyperbolic orbits and sets (37D05) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (4)

Eventual shadowing for chain transitive sets of $C^1$ generic dynamical systems ⋮ Expansive homoclinic classes of generic \(C^{1}\)-vector fields ⋮ Robustly measure expansiveness for C¹ vector fields ⋮ Continuum-wise expansive homoclinic classes for robust dynamical systems

Cites Work

• One-parameter flows with the pseudo-orbit tracing property
• On the hyperbolicity of homoclinic classes
• \(C^1\)-stably expansive flows
• Nonsingular star flows satisfy Axiom A and the no-cycle condition
• Expansive one-parameter flows
• ROBUSTLY SHADOWABLE CHAIN COMPONENTS OF C¹VECTOR FIELDS
• Perturbations of the derivative along periodic orbits
• Robustly expansive codimension-one homoclinic classes are hyperbolic
• Expansive homoclinic classes
• Robustly expansive homoclinic classes

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