Torus structure in higher-dimensional Hamiltonian systems.

Abstract

Island tori of coupled standard maps are investigated. The study of invariants of the tangent map shows that the tori are embedded in higher-dimensional topological spheres. A new numerical method, the ``quasisurface of sections'' construction, reveals the torus structure in the nonlinear domain. Scaling laws and estimates for island boundaries are obtained. Arnold diffusion out of the island is found to be nonexistent or exceedingly slow. The measure of phase space occupied by islands versus that occupied by chaotic trajectories is shown to decline rapidly as the number of degrees of freedom increases.