Abstract
A computer has been used to determine the stability character of periodic orbits for the Hamiltonian oscillator system H=12(p12+p22+q12+q22)+q12q2−13q23. Using procedures developed by Greene [J. Math. Phys. 9, 760 (1968)], empirical evidence has been obtained indicating that this system has a dense or near dense set of unstable periodic orbits throughout its stochastic (unstable) regions of phase space. The extent to which such stochastic regions exhibit C-system behavior, i.e., ergodicity and mixing, is discussed. Finally, the above Hamiltonian system is shown to be intimately related to the Fermi-Pasta-Ulam system as well as to the Toda lattice.
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