Smooth TA-maps with robust shadowing are Axiom A

DOI10.1007/s10883-021-09579-6OpenAlexW3214697738WikidataQ114017538 ScholiaQ114017538MaRDI QIDQ2694488

Seyed Mohsen Moosavi, Khosro Tajbakhsh

Publication date: 3 April 2023

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10883-021-09579-6

zbMATH Keywords

Axiom Ahyperbolicityendomorphismshadowingstable shadowing

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Generic properties, structural stability of dynamical systems (37C20)

Cites Work

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• Pseudo-orbit tracing property and strong transversality of diffeomorphisms on closed manifolds
• Topological Anosov maps of infra-nil-manifolds
• An ergodic closing lemma
• Orbital and weak shadowing properties
• Classification of special Anosov endomorphisms of nil-manifolds
• Sets of dynamical systems with various limit shadowing properties
• HYPERBOLICITY OF CHAIN TRANSITIVE SETS WITH LIMIT SHADOWING
• The C¹ closing lemma for non-singular endomorphisms
• Diffeomorphisms satisfying the specification property
• Anosov endomorphisms
• Persistent Manifolds are Normally Hyperbolic
• Continuum-wise expansiveness for generic diffeomorphisms
• Continuous inverse shadowing and hyperbolicity
• Endomorphisms of Compact Differentiable Manifolds
• Necessary Conditions for Stability of Diffeomorphisms

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