Continuous inverse shadowing and hyperbolicity

DOI10.1017/S0004972700033487zbMath1023.37010MaRDI QIDQ4807981

Keon-Hee Lee

Publication date: 5 November 2003

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Anosov diffeomorphismsshadowinginverse shadowingstructurally stable diffeomorphisms

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50)

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Divergence-free vector fields with inverse shadowing ⋮ Volume-preserving diffeomorphisms with inverse shadowing ⋮ Symplectic diffeomorphisms with inverse shadowing ⋮ Shadowing, internal chain transitivity and \(\alpha \)-limit sets ⋮ Inverse shadowing and related measures ⋮ Smooth TA-maps with robust shadowing are Axiom A ⋮ Unnamed Item ⋮ Expansivity and unique shadowing ⋮ Topological stability and shadowing of zero-dimensional dynamical systems ⋮ Various types of shadowing and specification on uniform spaces ⋮ C²-stably inverse shadowing diffeomorphisms ⋮ Inverse shadowing for structurally stable flows ⋮ Preservation of shadowing in discrete dynamical systems ⋮ On inverse shadowing ⋮ Relations between shadowing and inverse shadowing in dynamical systems ⋮ When is the beginning the end? On full trajectories, limit sets and internal chain transitivity ⋮ Unnamed Item ⋮ Orbital shadowing, \(\omega\)-limit sets and minimality ⋮ Inverse pseudo orbit tracing property for robust diffeomorphisms

Cites Work

• Approximate and real trajectories for generic dynamical systems
• Topologically stable homeomorphisms of the circle
• Persistence in expansive systems
• The topological stability of diffeomorphisms
• Diffeomorphisms in ℱ¹(M) satisfy Axiom A
• Filtrations, Decompositions, and Explosions
• Diffeomorphisms with persistency

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