Extraction of a Collective Submanifold for the Hénon-Heiles System

Abstract

1351The maximal-decoupling procedure of ~ collective submanifold fQrmulated within the framework of the time·dependent Hartree·Fock theory is applied to a classical Hamiltonian system numerically investigated by Henon and Heiles. The periodic orbits are obtained from the condition that the terms with zero denominators vanish in the collective Hamiltonian and they are in agreement with the numerical results by computer simulation. at University of Hawaii -Manoa on June 29, 2015 http://ptp.oxfordjournals.org/ Downloaded from 1352 K. Takabayashi*) The self-consistent collective-coordinate method (SeC), which has been developed in Refs. 2) and 3), extracts a collective submanifold by the so-called invariance principle of the (time-dependent) Schrodinger equation, while the present formulation does the same thing by imposing a maximal-decoupling condition on the classical canonical equations of motion to which the TDHF equation reduces_ at University