In this paper we prove that any C1 vector field defined on a three-dimensional manifold can be approximated by one that is uniformly hyperbolic, or that exhibits either a homoclinic tangency or a singular cycle. This proves an analogous statement of a conjecture of Palis for diffeomorphisms in the context of C1-flows on three manifolds. For that, we rely on the notion of dominated splitting for the associated linear Poincaré flow.
|Original language||English (US)|
|Number of pages||37|
|Journal||Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire|
|State||Published - 2003|
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Applied Mathematics