Hyperbolicity, transitivity and the two-sided limit shadowing property

DOI10.1090/S0002-9939-2014-12250-7zbMath1346.37029arXiv1301.2356MaRDI QIDQ5496306

Bernardo Carvalho

Publication date: 30 January 2015

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

Full work available at URL: https://arxiv.org/abs/1301.2356

zbMATH Keywords

transitivityhyperbolicitypseudo-orbitshadowinglimit shadowing

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Generic properties, structural stability of dynamical systems (37C20) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Dynamical systems involving smooth mappings and diffeomorphisms (37C05) Morse-Smale systems (37D15)

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Cites Work

• Generalizations of analogs of theorems of Maizel and Pliss and their application in shadowing theory
• \( C^1\)-stable shadowing diffeomorphisms
• Lyapunov functions and topological stability
• Ergodic theory on compact spaces
• Stability theorems and hyperbolicity in dynamical systems
• Shadowing in dynamical systems
• Pseudo-orbit shadowing in the \(C^1\) topology
• Sets of dynamical systems with various limit shadowing properties
• Diffeomorphisms satisfying the specification property
• Expansive homoclinic classes
• Diffeomorphisms in ℱ¹(M) satisfy Axiom A
• Expansive Homeomorphisms and Topological Dimension
• Limit shadowing property
• On Codimension One Anosov Diffeomorphisms
• Necessary Conditions for Stability of Diffeomorphisms
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• Unnamed Item

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