3 problems

Dominant-harmonic splitting conjecture. For $\nu\in(\nu_0,\nu_1)$,

Consider an integrable system whose parameters vary slowly in time, with the associated invariant manifolds, separatrix splitting, and homoclinic intersections defined analogously…

Generic graph separatrix conjecture. For a generic trigonometric polynomial $V$, the associated Hamiltonian system has a hyperbolic critical point whose invariant manifolds coincid…