The structure on invariant measures of \(C^{1}\) generic diffeomorphisms

DOI10.1007/S10114-011-9723-5zbMath1334.37026arXiv1004.3439OpenAlexW3100960079MaRDI QIDQ270311

Xue Ting Tian, Wen Xiang Sun

Publication date: 7 April 2016

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.3439

zbMATH Keywords

generic propertytopologically transitivehyperbolic basic setinvariant measure and periodic measureirregular point

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Partially hyperbolic systems and dominated splittings (37D30)

Related Items (4)

On density of ergodic measures and generic points ⋮ Different asymptotic behavior versus same dynamical complexity: recurrence \& (ir)regularity ⋮ Topological pressure for the completely irregular set of Birkhoff averages ⋮ Uniform hyperbolicity on random sets

Cites Work

• Unnamed Item
• Nonuniform hyperbolicity for \(C^{1}\)-generic diffeomorphisms
• Connecting invariant manifolds and the solution of the \(C^ 1\) stability and \(\Omega\)-stability conjectures for flows
• Generic properties of invariant measures for Axiom A diffeomorphisms
• Non-uniformly hyperbolic periodic points and uniform hyperbolicity forC¹diffeomorphisms
• Non-zero Lyapunov exponents and uniform hyperbolicity

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