5 problems

Let $G\subset \operatorname{Diff}_+^\omega(\mathbb S^1)$ be a locally discrete, finitely generated subgroup. The dichotomy in the classification theorem stated immediately before t…

Renormalisation hyperbolicity conjecture. The renormalisation operator $\mathcal{R}$, restricted to $\mathcal{E}_{\mathbf{c}}$, is hyperbolic when restricted to its attractor.

Rigidity conjecture. There is a full-measure set of decorated rotation numbers $\gamma$ such that, whenever $T_1$ and $T_2$ are circle diffeomorphisms with breaks having breaks of…

Let a finitely generated group of $C^2$ circle diffeomorphisms admit an exceptional minimal set $\Lambda$, meaning a minimal closed invariant subset of the circle that is homeomorp…

Let a finitely generated group act smoothly and minimally on the circle, meaning that every orbit is dense. Let Lebesgue measure denote the standard Lebesgue measure on the circle.…