Integrable approximation of regular regions with a nonlinear resonance chain

Abstract

Generic Hamiltonian systems have a mixed phase space where regions of regular and chaotic motion coexist. We present a method for constructing an integrable approximation to such regular phase-space regions including a nonlinear resonance chain. This approach generalizes the recently introduced iterative canonical transformation method. In the first step of the method a normal-form Hamiltonian with a resonance chain is adapted such that actions and frequencies match with those of the non-integrable system. In the second step a sequence of canonical transformations is applied to the integrable approximation to match the shape of regular tori. We demonstrate the method for the generic standard map at various parameters.

10 pages, 8 figures

References in corpus (2)

• Regular-to-chaotic tunneling rates using a fictitious integrable system
• Direct regular-to-chaotic tunneling rates using the fictitious integrable system approach

Cited by in corpus (2)

• Perturbation-Free Prediction of Resonance-Assisted Tunneling in Mixed Regular--Chaotic Systems
• Complex-Path Prediction of Resonance-Assisted Tunneling in Mixed Systems