  We discuss the recently achieved Bose-Einstein condensation for alkali-metal
atoms in magnetic traps. The theoretically predicted low-energy collective
oscillations of the condensate have been experimentally confirmed by laser
imaging techniques. We show by using Poincar\`e sections that at higher
energies non-linear effects appear and oscillations become chaotic. PACS
03.75.Fi, 05.30.Jp, 05.45.+b, 32.80.Pj
