Abstract
We study numerically Hamiltonians derived from the 3-particle Toda lattice by truncation at orders i ≤ 10. The third order system is the Hénon - Heiles (HH) Hamiltonian. The behavior of the systems of order 5, 7 and 9 is similar but their degree of stochasticity is smaller. In contrast with the HH system, they have appreciable ordered regions for energies larger than the escape energy. In all cases of odd order systems do not have an escape energy. The even order systems do not have an escape energy. The 4th order system seems integrable but all other systems show transition to a large degree of stochasticity. As the energy increases beyond E crit the stochastic regions increase, first abruptly and then more slowly. As the order i increases the systems tend to be integrable Toda lattice. The topology on the surface of section x = 0 is studied in detail. The changes of topology are related to changes in the stability character of the various periodic orbits.
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