A new integration method of Hamiltonian systems by symplectic maps

摘要: A perturbation theory is developed for constructing stroboscopic and Poincare maps Hamiltonian systems with a small perturbation. It based on canonical transformation by which the evolution becomes unperturbed during entire period while all perturbations are acting instantaneously one kick per period. Matching of solutions before after kicks establishes symplectic map exactly describes evolution. The generating function associated this satisfies Hamilton-Jacobi equations. solution equation found in first order theory. shown that reproduces correctly sections statistical properties typical orbits. well known perturbed twist mapping and, particular, standard may be obtained from symmetric as an approximation. method also applied to construct at arbitrary phase space. In particularly, describing motion near separatrix derived.