8 problems

Let … . KAM conjecture. If the Diophantine equation has only finitely many solutions, then a KAM type result holds for … , depending on a parameter which takes value in a Cantor-ty…

Let $V_N$ denote the relative phase-space volume of the union of KAM islands for an $N$-particle system at fixed energy density and fixed forcing parameters. Vanishing-of-islands c…

In the outer, retrograde configuration, let $\mathcal{D}_{{{{{{{{{\rm t} t} t} t} t} t} t} t} s}$ be the $8$-dimensional phase-space region almost completely filled with a positive…

An elliptic equilibrium is an elliptic fixed point of an analytic Hamiltonian system, and a KAM torus is an invariant quasi-periodic torus of such a system satisfying the KAM condi…

Fix an initial value $z(0)=z_0$. The $xy$-plane is divided into disjoint KAM and non-KAM regions, and a KAM region is one of the regions in which the associated trajectories are tr…

KAM existence conjecture. There exist three explicit functions $a,b_d,b_a:\mathbb R^+\to\mathbb R^+$ such that

A posteriori KAM existence conjecture. There exist three explicit functions $a,b_d,b_a:\mathbb R^+\to\mathbb R^+$ such that

Let $H$ be a real-analytic Hamiltonian with an elliptic equilibrium at the origin, and let $\alpha\in\mathbb R^n$ be the frequency vector of the linear part of the flow. Recall tha…