We investigate the collective oscillations of a Bose condensate in an aniso
tropic harmonic trap, We analytically calculate the values of the trap defo
rmation for which the normal modes are in resonance. In the presence of low
-order resonances, the amplitude dependence of frequencies is strongly enha
nced. We also study the transition to chaos of the collective modes as a fu
nction of the trap anisotropy. (C) 2000 Elsevier Science B.V. All rights re
served.