KAM surfaces computed from the Hénon-Heiles Hamiltonian

Publisher Website
Google Scholar
Abstract
The Hénon‐Heiles Hamiltonian is a well‐known example of a nonintegrable system with two degrees of freedom. As is usual with such systems, the Hamiltonian generates three different kinds of orbits. Periodic orbits close on themselves. Other orbits cover two dimensional manifolds known as KAM surfaces after Kolmogorov, Arnol’d and Moser. Finally, some orbits fill out a finite portion of a threee‐dimensional constant‐energy manifold in the phase space. In this paper the Hénon‐Heiles Hamiltonian is treated by the method of residues, a method that has been developed previously. The purpose of this calculation is to find where KAM surfaces exist. The method depends on the numerical calculation of the stability of periodic orbits, together with heuristic schemes of extrapolation, to estimate the stability of other nearby periodic orbits. The crucial assumption is that the existence of KAM surfaces depends on the stability of nearby periodic orbits. This assumption appears to be verified for the system treated here, as it has been for previous cases that have been tested.

This publication has 0 references indexed in Scilit: