Generic properties of vector fields identical on a compact set and
codimension one partially hyperbolic dynamics
Generic properties of vector fields identical on a compact set and
codimension one partially hyperbolic dynamics
Let $\mathscr{X}^r(M)$ be the set of $C^r$ vector fields on a boundaryless compact Riemannian manifold $M$. Given a vector field $X_0\in\mathscr{X}^r(M)$ and a compact invariant set $\Gamma$ of $X_0$, we consider the closed subset $\mathscr{X}^r(M,\Gamma)$ of $\mathscr{X}^r(M)$, consisting of all $C^r$ vector fields which coincide with $X_0$ on $\Gamma$. Study …