Uniform hyperbolicity of invariant cylinder

Abstract

For a nearly integrable Hamiltonian systems $H=h(p)+\epsilon P(p,q)$ 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 ${\sqrt{\epsilon }}^{1+d}$-neighborhood of finitely many double resonant points. It allows one to construct diffusion orbits to cross double resonance.

References in corpus (2)

• Homoclinic orbits and critical points of barrier functions
• A way to cross double resonance

Cited by in corpus (2)

• Lasry-Lions, Lax-Oleinik and Generalized characteristics
• A way to cross double resonance