Canonical stochastic web map.
In many Hamiltonian systems subjected to a time (or space) -periodic perturbation with a broad spectrum an approach is widely used of replacing the system by periodically delta -kicked dynamical systems, which allows us to reduce them to symplectic mappings. In this paper it is shown that this approach has a fundamental failure, and the corresponding mapping does not correctly describe the continuous original system. It is demonstrated on the example of the stochastic web map obtained by this approach to describe a periodically driven harmonic oscillator which exhibits non-Kolmogorov-Arnold-Moser chaos, particularly, the formation of stochastic webs. A correct canonical map corresponding to this system is obtained using a recently developed method based on the canonical transformation of variables [S. S. Abdullaev, J. Phys. A 35, 2811 (2002)]. Using a direct numerical integration of the system it is shown that the canonical map correctly describes the periodically driven harmonic oscillator with a finite number of spectrum modes.
Abdullaev
S S
SS
Institut für Energieforschung-Plasmaphysik, Forschungszentrum Jülich GmbH, EURATOM Association, Trilateral Euregio Cluster, D-52425 Jülich, Germany.