Asymptotic Expansion of the Homoclinic Splitting Matrix for the Rapidly, Quasiperiodically, Forced Pendulum
arXiv:0711.3654 · doi:10.1063/1.3398483
Abstract
We study a Hamiltonian describing a pendulum coupled with several anisochronous oscillators, devising an asymptotic expansion for the splitting (matrix) associated with a homoclinic point. This expansion consists of contributions that are manifestly exponentially small in the limit of vanishing hyperbolicity, by a shift-of-contour argument. Hence, we infer a similar upper bound on the splitting itself.
32 pages
References in corpus (7)
- KAM Theorem and Quantum Field Theory
- Pendulum: separatrix splitting
- Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems
- Melnikov's approximation dominance. Some examples
- A Renormalization Proof of the KAM Theorem for Non-Analytic Perturbations
- Construction of Whiskers for the Quasiperiodically Forced Pendulum
- Reminiscences on science at I.H.E.S. A problem on homoclinic theory and a brief review