On \(C^1\)-persistently expansive homoclinic classes

DOI10.3934/dcds.2006.14.465zbMath1110.37022OpenAlexW2136858688MaRDI QIDQ867390

Martín Sambarino, José L. Vieitez

Publication date: 15 February 2007

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2006.14.465

zbMATH Keywords

dominated splittingexpansivenesshomoclinic classeshypgerbolicity

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Generic properties, structural stability of dynamical systems (37C20) Partially hyperbolic systems and dominated splittings (37D30) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (18)

Hyperbolicity versus weak periodic orbits inside homoclinic classes ⋮ Expansive homoclinic classes of generic \(C^{1}\)-vector fields ⋮ On bi-Lyapunov stable homoclinic classes ⋮ Continuum-wise expansiveness for generic diffeomorphisms ⋮ Dominated splitting of differentiable dynamics with \(\mathrm{C}^1\)-topological weak-star property ⋮ Weak measure expansiveness for partially hyperbolic diffeomorphisms ⋮ Asymptotic measure expansive diffeomorphisms ⋮ Robustly measure expansiveness for C¹ vector fields ⋮ Continuum-wise expansive homoclinic classes for robust dynamical systems ⋮ Symbolic extensions and dominated splittings for generic \(C^1\)-diffeomorphisms ⋮ Unnamed Item ⋮ Chain components with stably limit shadowing property are hyperbolic ⋮ Hyperbolicity of \(C^{1}\)-star invariant sets for \(C^{1}\)-class dynamical systems ⋮ Periodically expansive homoclinic classes ⋮ Continuum-wise expansiveness for discrete dynamical systems ⋮ R-robustly measure expansive homoclinic classes are hyperbolic ⋮ Asymptotic measure-expansiveness for generic diffeomorphisms ⋮ Structurally stable homoclinic classes

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