SEMICLASSICAL DENSITY-OF-STATES AT SYMMETRICAL PITCHFORK BIFURCATIONS IN COUPLED QUARTIC OSCILLATORS

We analyze the quantum density of states for a system of coupled quartic oscillators in the vicinity of symmetric isochronous or pitchfork bifurcations of the primary oscillator modes. A uniform semiclassical expression for the contribution to the density of states from the set of periodic orbits involved in the bifurcation is derived following the approach of Ozorio de Almeida and Hannay [J. Phys. A 20, 5873 (1987)] and Ozorio de Almeida and Aguiar [Physica D 41, 391 (1990)].