A way to cross double resonance

Abstract

For typical perturbations of convex integrable Hamiltonian system with three degrees of freedom, a path of diffusion is established to cross strong double resonant point. Together with the uniform hyperbolicity of invariant cylinders got in \cite{C15}, one obtains a transition chain along which one is able to construct diffusion orbits suggested in \cite{A66}.

arXiv admin note: substantial text overlap with arXiv:1207.4016

References in corpus (3)

• Homoclinic orbits and critical points of barrier functions
• Arnold diffusion in nearly integrable Hamiltonian systems of arbitrary degrees of freedom
• Uniform hyperbolicity of invariant cylinder

Cited by in corpus (3)

• Arnold diffusion in nearly integrable Hamiltonian systems of arbitrary degrees of freedom
• Lasry-Lions, Lax-Oleinik and Generalized characteristics
• Uniform hyperbolicity of invariant cylinder