ON THE STABILIZATION OF STRING-OSCILLATOR INTERACTION

We consider the system of equations that describes crosswise oscillati ons of an infinite string subject to transversal forces at a finite nu mber N of points. We prove that the string tends to stationary states as t --> +/-infinity. A brief description of this result was published in [11]. In [8]-[10] a similar result was obtained for the case N = 1 . These results describe a quantization for the infinite-dimensional H amiltonian systems under consideration.