Usual limit shadowable homoclinic classes of generic diffeomorphisms

DOI10.1186/1687-1847-2012-91zbMath1285.37007OpenAlexW2154899090WikidataQ59289231 ScholiaQ59289231MaRDI QIDQ2448047

Manseob Lee

Publication date: 29 April 2014

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2012-91

zbMATH Keywords

hyperbolichomoclinic class\(C^1\)-genericusual limit shadowing

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Generic properties, structural stability of dynamical systems (37C20) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Asymptotic properties of solutions to ordinary differential equations (34D05) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items

Eventual shadowing for chain transitive sets of $C^1$ generic dynamical systems ⋮ Hyperbolicity and types of shadowing for \(C^1\) generic vector fields ⋮ Unnamed Item ⋮ Lyapunov stable homoclinic classes for smooth vector fields ⋮ The ergodic shadowing property from the robust and generic view point ⋮ CHAIN COMPONENTS WITH THE STABLE SHADOWING PROPERTY FOR C¹ VECTOR FIELDS ⋮ Asymptotic orbital shadowing property for diffeomorphisms

Cites Work

• Nonuniform hyperbolicity for \(C^{1}\)-generic diffeomorphisms
• Periodic orbits and chain-transitive sets of \(C^1\)-diffeomorphisms
• Shadowing in dynamical systems
• An ergodic closing lemma
• Pseudo-orbit shadowing in the \(C^1\) topology
• Sets of dynamical systems with various limit shadowing properties
• GENERIC DIFFEOMORPHISMS WITH ROBUSTLY TRANSITIVE SETS
• SHADOWABLE CHAIN TRANSITIVE SETS OF C¹-GENERIC DIFFEOMORPHISMS
• Diffeomorphisms satisfying the specification property
• Expansive homoclinic classes
• Diffeomorphisms in ℱ¹(M) satisfy Axiom A
• Limit shadowing property