3 problems

Higher-order singular-hyperbolicity conjecture. Analogous results should hold for singular hyperbolic sets of every order $p$ with $2\leq p\leq \operatorname{dim}F$. The paper deve…

Arbieto's conjecture. The nonwandering set of a $C^1$ generic star flow is the disjoint union of finitely many transitive sets which are positively or negatively sectional-hyperbol…

Let $M^d$ be a compact manifold, let $X\in {\cal X}^1(M^d)$ be a vector field, and let ${\cal X}^*(M^d)$ denote the set of star vector fields, namely those having a $C^1$ neighborh…