9 problems

Let $\gamma_1$ and $\gamma_2$ be critical invariant circles in the same universality class, and let $h_{\gamma_i}$ be their conjugacies to the reference dynamics. Write…

Let $\gamma_1$ and $\gamma_2$ be critical invariant circles, and let $G_{\gamma_1,\gamma_2}$ and $H_{\gamma_1,\gamma_2}$ denote the associated maps between them. Let…

Let $g$, $h$, and $h^{-1}$ be the conjugacies associated with a critical invariant circle, and let $\kappa(\cdot)$ denote their regularity. A numerical characteristic is universal…

Let $R$ denote a critical invariant circle, and let $\kappa(R)$ denote its regularity. A numerical characteristic is universal when it takes the same value on an open set of functi…

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…

Conjecture A. The set $\Omega_{P} \cup \Omega_{Q}$ of pairs $(a,b)$ for which $T_{ab}$ is either periodic or has a piecewise conic invariant circle is dense in $\Omega_{SB}$.

Finite differentiability conjecture. At the breakdown, there is a finitely differentiable invariant circle.

Let $x$ be an irrational number and let the standard family be the usual one-parameter family of area-preserving maps. The Brjuno condition is the convergence condition … where…

Greene's golden-mean conjecture. The rotation number of the critical invariant curve is equal to the golden mean: