Generic properties of vector fields identical on a compact set and codimension one partially hyperbolic dynamics

Shaobo Gan, Ruibin Xi, Jiagang Yang +1

Let ${\mathcal{X}}^r(M)$ be the set of $C^r$ vector fields on a boundaryless compact Riemannian manifold $M$. Given a vector field $X_0\in {\mathcal{X}}^r(M)$ and a compact invariant se…