5 problems

Let $F$ be a smooth vector field on $S^3$ generating a heteroclinic knot $H$, and suppose that $Ess(F)$ with respect to $H$ is finite, possibly empty. An invariant set…

Consider Bianchi type VIII and IX models in the supercritical case $v\in(1/2,1)$, let $C$ be the Cantor set associated with infinite Bianchi type II heteroclinic chains, and let…

Consider Bianchi type VIII and IX models in the supercritical case $v\in(1/2,1)$, with time parameter satisfying $\tau_-\to\infty$. Period-two stable-set conjecture. Each heterocli…

Ashwin–Chossat conjecture. For a closed heteroclinic cycle among equilibria $\xi_1,\ldots,\xi_m$ satisfying (Ha)–(Hd) and (3), generically, the principal heteroclinic cycle is an a…

Consider the HL Bianchi models with parameter $1/2<v<1$, whose Kasner circle has stable arcs where heteroclinic chains terminate. HL analogue of the BKL conjecture. The asymptotic…