Robustly chain transitive sets with orbital shadowing diffeomorphisms

DOI10.1080/14689367.2012.725032zbMath1256.37008OpenAlexW2080174657MaRDI QIDQ4648280

Manseob Lee

Publication date: 8 November 2012

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14689367.2012.725032

zbMATH Keywords

hyperbolicshadowingtransitivechain transitivebasic setorbital shadowing

Mathematics Subject Classification ID

Generic properties, structural stability of dynamical systems (37C20) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Symbolic dynamics (37B10) Partially hyperbolic systems and dominated splittings (37D30)

Related Items

Unnamed Item ⋮ Hamiltonian systems with orbital, orbital inverse shadowing ⋮ Orbital shadowing property on chain transitive sets for generic diffeomorphisms ⋮ Unnamed Item ⋮ Unnamed Item ⋮ CHAIN COMPONENTS WITH THE STABLE SHADOWING PROPERTY FOR C¹ VECTOR FIELDS

Cites Work

• Stability theorems and hyperbolicity in dynamical systems
• Contributions to the stability conjecture
• A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources
• Partial hyperbolicity and robust transitivity
• Shadowing in dynamical systems
• An ergodic closing lemma
• Orbital and weak shadowing properties
• A robustly chain transitive attractor with singularities of different indices
• Flows with the (asymptotic) average shadowing property on three-dimensional closed manifolds
• Sinai–Ruelle–Bowen measures for N-dimensional derived from Anosov diffeomorphisms
• Diffeomorphisms satisfying the specification property