Periodic orbits and expansiveness

DOI10.1007/s00209-010-0767-5zbMath1263.37037OpenAlexW2015989386MaRDI QIDQ658351

Alexander Arbieto

Publication date: 12 January 2012

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-010-0767-5

zbMATH Keywords

generic propertiesexpanding mapsexpansivenessexpanding periodic pointspositive expansiveness

Mathematics Subject Classification ID

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

Related Items (26)

Generic diffeomorphisms with weak limit shadowing ⋮ Eventual shadowing for chain transitive sets of $C^1$ generic dynamical systems ⋮ General expansiveness for diffeomorphisms from the robust and generic properties ⋮ Unnamed Item ⋮ Generic expansive Hamiltonian systems ⋮ Continuum-wise expansiveness for generic diffeomorphisms ⋮ Expansive measures versus Lyapunov exponents ⋮ Robust periodic stability implies uniform exponential stability of Markovian jump linear systems and random linear ordinary differential equations ⋮ POSITIVELY WEAK MEASURE EXPANSIVE DIFFERENTIABLE MAPS ⋮ Generic Bowen-expansive flows ⋮ Robustly measure expansiveness for C¹ vector fields ⋮ Symbolic extensions and dominated splittings for generic \(C^1\)-diffeomorphisms ⋮ Unnamed Item ⋮ Expansive transitive sets for robust and generic diffeomorphisms ⋮ Measure expansivity for \(C^1\)-conservative systems ⋮ Spectral decomposition and stability of mild expansive systems ⋮ Continuum-wise expansiveness for discrete dynamical systems ⋮ Continuum-wise expansive symplectic diffeomorphisms ⋮ R-robustly measure expansive homoclinic classes are hyperbolic ⋮ The ergodic shadowing property from the robust and generic view point ⋮ Asymptotic measure-expansiveness for generic diffeomorphisms ⋮ Orbital shadowing for \(C^1\)-generic volume-preserving diffeomorphisms ⋮ Asymptotic orbital shadowing property for diffeomorphisms ⋮ Volume-Preserving Diffeomorphisms with Various Limit Shadowing ⋮ EXPANDING MEASURES FOR HOMEOMORPHISMS WITH EVENTUALLY SHADOWING PROPERTY ⋮ Continuum-wise expansive diffeomorphisms and conservative systems

Cites Work

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• Positively expansive differentiable maps
• Robustly expansive homoclinic classes are generically hyperbolic
• A proof of the \(C^ 1\) stability conjecture
• The ergodic closing lemma for \(C^ 1\) regular maps
• Positively expansive homeomorphisms of compact spaces
• An ergodic closing lemma
• Generic Bowen-expansive flows
• On persistently positively expansive maps
• Expansive homoclinic classes
• Diffeomorphisms in ℱ¹(M) satisfy Axiom A
• Non-zero Lyapunov exponents and uniform hyperbolicity
• C¹-Stably Positively Expansive Maps
• Endomorphisms of Compact Differentiable Manifolds
• Necessary Conditions for Stability of Diffeomorphisms

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