A REVIEW STUDY OF THE 3-PARTICLE TODA LATTICE AND HIGHER-ORDER TRUNCATIONS: THE ODD-ORDER CASES — PART I

Abstract

The numerical behavior of the truncated 3-particle Toda lattice (3pTL) is reviewed and studied in more detail (than in previous papers) and at higher energies (at odd-orders n ≤ 9). We further extended our study to higher truncations at odd-orders, n = 2k + 1, k = 1, …, 9. We have located the majority of the families of periodic orbits along with their main bifurcations. By using: (a) the method of Poincaré surface of section, (b) the maximum Lyapunov characteristic number and (c) the ratio of the families of ordered periodic orbits, we studied the topology of the nine odd-order Hamiltonians with respect to their order of truncation.