9 problems

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 $\rho\in\mathbb{R}\setminus\mathbb{Q}$ be an irrational rotation number, and suppose that the corresponding Mather set is a Cantori. Let $\Delta_1(\rho)$ denote the associated…

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…

Large-mean-forcing integrability conjecture. For fixed $V$ and $\sigma(F)$, there is an $F_{c}$ such that, for all $\overline{F}\geq F_{c}$, the map $f_{V,F}$ is integrable.

Consider invariant circles of a twist map, each with a rotation vector, and call a rotation vector noble when it belongs to the noble class associated with the golden mean. MacKay'…

Let an USF map be a map of the type considered in the paper, and let a mini--maximizing $(p,q)$--type periodic orbit have twist number $-1/2$. A USF obstruction conjecture asserts…

Let the standard map be the area-preserving twist map under consideration, and let $\Gamma_0$ denote its symmetry line. A total dominant symmetry-line conjecture asserts that…