The star systems \({\mathcal H}^*\) and a proof of the \(C^1 \Omega\)-stability conjecture for flows
This paper is devoted to a new proof the \(C^1\Omega\) stability for flows, which is formulated in the following way: Let \(M\) be a compact \(n\)-dimensional \(C^\infty\)-Riemannian manifold without boundary \((n>1)\). Denote by \(X=X^1(M)\) the set of all \(C^1\) vector fields on \(M\), endowed with \(C^1\) topology. Let \(S\) be a \(C^1\) vector field on \(M\). If \(S\) is \(C^1\Omega\)-stable then \(S\) satisfies Axiom A and the no-cycle condition. Here the author solves this crucial point, which is considerably different from the approach of Hayashi or Wen and based on Liao`s obstruction set theory.
scientific article; zbMATH DE number 1454723
scientific article