3 problems

Let $f$ be a $C^r$ partially hyperbolic diffeomorphism on a compact manifold $M$, with $r\geq 2$. The distribution $E^s_f$ is stably $C^1$ if, for every…

Let a partially hyperbolic system have a center foliation $W^c$, when it exists. Typical-system conjecture. For typical partially hyperbolic systems, the center foliation is not ab…

Let $G$ be a $C^2$ vector field with a partially hyperbolic attracting set $\Lambda=\Lambda_G(U)$, and suppose that the non-uniform sectional expansion condition holds on a positiv…