Another proof for \(C^1\) stability conjecture for flows

DOI10.1007/BF02871842zbMath0922.58037OpenAlexW2044034474WikidataQ123026047 ScholiaQ123026047MaRDI QIDQ1286701

Shaobo Gan

Publication date: 11 October 1999

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02871842

zbMATH Keywords

Axiom Aobstruction setstability conjecture\(C^1\)-connecting lemmaminimal rambling set

Mathematics Subject Classification ID

Stability theory for smooth dynamical systems (37C75)

Related Items (8)

Vector fields with the oriented shadowing property ⋮ Weakly shadowable vector fields on non-oriented surfaces ⋮ Weak shadowing property for flows on oriented surfaces ⋮ Vector fields with topological stability ⋮ Nonsingular star flows satisfy Axiom A and the no-cycle condition ⋮ Interiors of sets of vector fields with shadowing corresponding to certain classes of reparameterizations ⋮ Newhouse phenomenon and homoclinic classes ⋮ Hyperbolicity in the volume-preserving scenario

Cites Work

• Connecting invariant manifolds and the solution of the \(C^ 1\) stability and \(\Omega\)-stability conjectures for flows
• Structural stability on two-dimensional manifolds
• A proof of the \(C^ 1\) stability conjecture
• An ergodic closing lemma
• On the \(C^ 1\) stability conjecture for flows
• Structurally stable differential systems
• A Proof of C 1 Stability Conjecture for Three-Dimensional Flows
• The stability theorems for discrete dynamical systems on two-dimensional manifolds
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