Mode fluctuation distribution of coupled quartic oscillators

The mode fluctuation distribution (MFD) of a system of two quartic oscillat ors coupled by a quartic pertur bation is numerically studied. The coupling strength serves as a control parameter to simulate the transition from int egrable to chaotic regimes. It is demonstrated that even in this potential system the MFD turns out to be a very sensitive measure, as it manifests th e same transformation seen in billiard systems. It is characterized by Gaus sian and skewed distributions in the regions, known to be chaotic and integ rable, respectively, from classical Poincare sections and quantum-mechanica l level spacing statistics. In the intermediate regions where the KoI'mogor oV-Amol'd-Moser tori survive, the MFD has various distorted forms. [A1063-6 51X(98)04712-6].