Chaos-Order-Chaos Transitions in a Two-Dimensional Hamiltonian System

We present a new result which shows the transitions from chaos to order and again to chaos as the coupling parameter between two nonlinearly coupled oscillators of a Hamiltonian system is varied continuously from $-\infty \mathrm{to} +\infty$. By exploiting the symmetry of the system, we show that there is no general correspondence between the classical chaotic motion and the Gaussian-orthogonal-ensemble distributions of the energy-level fluctuations of the corresponding quantum system.