Accessibility and Centralizers for Partially Hyperbolic Flows

The paper proves that C1-stable accessibility is C1-dense among partially hyperbolic flows in the four categories via a two-part scheme: (i) global c-sections given by c-admissible disk families for nearby bisaturated sets (Proposition 3.9), and (ii) a flow-specific local perturbation that creates Brin quadrilaterals on those disks while preserving the category (Lemma 3.15). These feed into Proposition 3.11 and Theorem 3.1 to yield Theorem 1.1 . The candidate solution mirrors this blueprint: it uses global section families for the flow via time-1 maps, performs category-preserving local perturbations in disjoint flow boxes to implement Brin quadrilaterals, and then promotes disk-level accessibility to the whole bisaturated set. Minor imprecision aside (calling c-sections “global s/u-sections” and assuming a common disk for two arbitrary points before invoking the small-disk machinery), the method matches the paper’s argument in substance.