1. The problem statement, all variables and given/known data The center of a circular billiard is harmonically oscillating in horizontal direction with the amplitude a and frequency omega. Describe the motion of elastic particle with mass m in this billiard. Use the proper phase space and Poincare map. Under what conditions, dimensionless parameter eta=r/R, is energy of the system time limited and when time unlimited and when is the motion chaotic? Does any one has experience with this kind of problems?