Uniform hyperbolicity of invariant cylinder

Abstract

For a positive definite Hamiltonian system $H = h(p) + \epsilon P (p, q)$ with $(p, q) \in \mathbb{R}^3 \times \mathbb{T}^3$, large normally hyperbolic invariant cylinders exist along the whole resonant path, except for the $\epsilon^{\frac{1}{2}+d}$ neighborhood of finitely many double resonant points. It allows one to construct diffusion orbits to cross double resonance.