Integrable approximation of regular regions with a nonlinear resonance chain
arXiv:1407.2513 · doi:10.1103/PhysRevE.90.052906
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.
arXiv comment10 pages, 8 figures
References in corpus (11)
- Resonance-assisted tunneling in near-integrable systems
- Resonance-Assisted Tunneling
- Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime
- Resonance- and chaos-assisted tunneling in mixed regular-chaotic systems
- Regular-to-chaotic tunneling rates using a fictitious integrable system
- Direct regular-to-chaotic tunneling rates using the fictitious integrable system approach
- The efficient computation of transition state resonances and reaction rates from a quantum normal form
- Complex paths for regular-to-chaotic tunneling rates
- Semiclassical description of resonance-assisted tunneling in one-dimensional integrable models
- Normal forms and complex periodic orbits in semiclassical expansions of Hamiltonian systems
- Integrable Approximation of Regular Islands: The Iterative Canonical Transformation Method