Stably inverse shadowable transitive sets and dominated splitting

DOI10.1090/S0002-9939-2011-10882-7zbMath1253.37002MaRDI QIDQ5388801

Keon-Hee Lee, Manseob Lee

Publication date: 20 April 2012

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

zbMATH Keywords

genericitydominated splitting

Mathematics Subject Classification ID

Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Partially hyperbolic systems and dominated splittings (37D30) Research exposition (monographs, survey articles) pertaining to dynamical systems and ergodic theory (37-02)

Related Items

Symplectic diffeomorphisms with limit shadowing ⋮ Unnamed Item ⋮ Hamiltonian systems with orbital, orbital inverse shadowing ⋮ Stably asymptotic average shadowing property and dominated splitting ⋮ CHAIN COMPONENTS WITH THE STABLE SHADOWING PROPERTY FOR C¹ VECTOR FIELDS ⋮ Inverse pseudo orbit tracing property for robust diffeomorphisms

Cites Work

• A \(C^1\)-generic dichotomy for diffeomorphisms: weak forms of hyperbolicity or infinitely many sinks of sources
• An ergodic closing lemma
• A Franks’ lemma that preserves invariant manifolds
• Stably weakly shadowing transitive sets and dominated splittings
• C¹-STABLE INVERSE SHADOWING CHAIN COMPONENTS FOR GENERIC DIFFEOMORPHISMS
• Characterisations of Ω-stability and structural stability via inverse shadowing
• Perturbations of the derivative along periodic orbits
• Diffeomorphisms in ℱ¹(M) satisfy Axiom A
• Inverse shadowing of circle maps
• Necessary Conditions for Stability of Diffeomorphisms