6 problems

The gyrokinetic phase-space one-form is treated using canonical coordinates adapted to the magnetic-field geometry. In contrast with constructions under regularity or near-axisymme…

Generality conjecture. The constructed solution is the general solution at low energies.

Let $g$ be a Riemannian or pseudo-Riemannian metric on an $m$-dimensional manifold $M$, let $g_0$ denote the flat metric, and let $\mathcal{R}_{m,r,s}(g)$ be the space of rational…

Consider a generalized Hamiltonian system in a three-dimensional phase space, with $N=3$ and $n\geq 3$; the same construction is stated to apply for $N>3$. Generalized Hamiltonian-…

Conjecture 2. The ranks of the gauge-transformation matrix and the Hamiltonian constraint distribution agree:

Consider the Hamiltonian system with Hamiltonian $H(q,p)=pq^2$, primitive conditions $q_0(t)$ and $p_0(t)$, and recursively defined series solutions … Write $\hat{q}_0(t)$ and…