5 problems

The characteristic map is a homeomorphism on the invariant set, with values in a cylinder. Canonical extension conjecture. The map $\widetilde{T}$ can be canonically extended to a…

Consider the renormalization operator acting on the class of twist maps under discussion, and call a property universal when it holds on an open set of functions. A fixed point is…

Let $\rho$in$(0,1)$ be a Diophantine number, and let $F$ be a twist map of the form given in the source. Denote by $\Lambda(\rho)$ the parameter threshold at which the invariant ci…

Let $F$ be a twist map, let $c_1<c_2$, and let $\Lambda_{[c_1,c_2]}$ be the set of orbits corresponding to minimal configurations with $c\in[c_1,c_2]$. Let $\alpha$ denote the rele…

Let $\Delta_0$ and $\Delta_1$ denote the instability quantities associated with an area-preserving twist diffeomorphism, and let $V$ be a $C^2$ potential. Instability-gap conjectur…