Melkinov's Method and Arnold Diffusion for Perturbations of Integrable Hamiltonian Systems.
Abstract
We start with an unperturbed system containing a homoclinic orbit and at least two families of periodic orbits associated with action angle coordinates. We use KAM theory to show that some of the resulting tori persist under small perturbations and use a vector of Melkinov integrals to show that, under suitable hypotheses, their stable and unstable manifolds intersect transversally. This transverse intersection is ultimately responsible for Arnold diffusion on each energy surface. The method is applied to a pendulum-oscillator systems. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1981
- Accession Number
- ADA103563
Entities
People
- Jerrold E. Marsden
- Philip Holmes
Organizations
- University of California, Berkeley