Conservative difference formulations of Calogero and Toda Hamiltonian systems

Abstract

Calogero and Toda Hamiltonian systems are reformulated using only differences. The formulations prove to have the same fundamental invariants as the continuous systems and, in addition, are readily implementable on modern digital computers.

Arbitrary order, Hamiltonian conserving numerical solutions of Calogero and Toda systems

“…[5, 10, l1] In previous Papent the second author has presented conservative difference methods of the second order applied to a number of dynamical systems (see e.g. [2J and [3]), among others to Calogero and Toda Hamiltonian Systems [4], while the first author has considered arbitrary high order methods conserving the energy or the Jacobi constant in gravitational problems (see e.g. [6][7][8]).…”