9 problems

Consider generic $C^1$ vector fields having a sectional-hyperbolic attracting set. Let the bounds referred to in Theorem and Corollary be the corresponding bounds for the number of…

Let a sectional-hyperbolic attracting set be $C^1$ close to a sectional-hyperbolic attractor, with no dimensional restrictions; equivalently, allow any combination of stable and ce…

Let a sectional-hyperbolic attracting set be an attracting set with stable and center-unstable dimensions satisfying $d_s\geq 1$ and $d_{cu}\geq 2$, and replace Lorenz-like singula…

Robust expansiveness conjecture. Theorem is still true for all $C^1$ vector fields exhibiting a sectional hyperbolic attracting set.

Basin equality conjecture. For any sectional-hyperbolic attracting set $\Lambda$, the topological basin of attraction coincides with the family of stable manifolds through the poin…

Let $X$ be a $C^1$ vector field with flow $X_t$, and let $\Gamma$ be a $p$-sectional hyperbolic set with invariant splitting $T_\Gamma M=E\oplus F$. A metric is required to provide…

Consider a $C^2$ flow with a general sectional-hyperbolic attracting set and a neighborhood of that attracting set. Let Lebesgue measure be compared with the physical measures, and…

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…

Consider smooth singular flows in dimensions higher than three that are sectionally-hyperbolic, meaning that they belong to the higher-dimensional class described in the source, ge…