Abstract
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 $\ensuremath{-}\ensuremath{\infty} \mathrm{to} +\ensuremath{\infty}$. 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.
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