C1-stably shadowable chain components

DOI10.1017/S0143385707000570zbMath1147.37015MaRDI QIDQ3509963

Kazuhiro Sakai

Publication date: 25 June 2008

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

shadowing propertyhyperbolic periodic pointhomoclinic tangencieschain componentheterodimensional cycles\( C^1 \)-stabilityhyperbolic-like property

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Partially hyperbolic systems and dominated splittings (37D30) Stability theory for smooth dynamical systems (37C75) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (12)

Eventual shadowing for chain transitive sets of $C^1$ generic dynamical systems ⋮ On the topology of the chain recurrent set of a dynamical system ⋮ Stably average shadowable homoclinic classes ⋮ Dominated splitting of differentiable dynamics with \(\mathrm{C}^1\)-topological weak-star property ⋮ Chain components with \(C^1\)-stably orbital shadowing ⋮ Unnamed Item ⋮ Chain components with stably limit shadowing property are hyperbolic ⋮ Stable weakly shadowable volume-preserving systems are volume-hyperbolic ⋮ Hyperbolicity of \(C^{1}\)-star invariant sets for \(C^{1}\)-class dynamical systems ⋮ Periodically expansive homoclinic classes ⋮ Codimension one structurally stable chain classes ⋮ R-robustly measure expansive homoclinic classes are hyperbolic

Cites Work

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• Homoclinic tangencies and dominated splittings
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• Recurrence and genericity

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