Finite energy states for periodically kicked nonlinear oscillator

We study a nonlinear oscillator interacting with a one-mode cavity field. W e assume, that the cavity is periodically kicked by a series of ultra-short coherent pulses. We show that for a special choice of parameters the syste m evolution is restricted to a finite set of n-photon states. In consequenc e, the mean energy of the cavity remains finite despite the fact that the c avity is continuously pumped. We study the properties of the cavity field s howing that the field exhibits nonclassical features.