Effects of bifurcations on the energy level statistics for oval billiards

We studied the energy level statistics for one parameter family of oval bil liards whose classical phase space consists of some regular and some irregu lar components. As the parameter is varied, a transition from an integrable system to a strongly chaotic one occurs with successive bifurcations. We a pplied the Berry-Robnik formula to the level-spacing distributions for a va riety of shapes of quantum oval billiards and found some striking effects o f bifurcations in the classical mechanical systems on the level-spacing dis tributions. The validity of the Berry-Robnik formula is also checked for th ose shapes of the oval billiard for which there exist two separated chaotic components in the phase space.