Periodic and quasiperiodic solutions of a forced discontinuous oscillator (Q6608689)

Many classical physical models are described by nonsmooth systems, including the Fermi-Ulam model describing the motion of a particle between two moving walls, billiard ball systems in the plane, a bouncing ball moving vertically, and oscillators with discontinuous or asymmetrical restoring forces. For those systems, a fundamental problem is determining the existence of periodic and quasiperiodic solutions.\N\NThe authors consider a forced oscillator with a discontinuous restoring force. By the Aubry-Mather theory they prove the existence of infinitely many periodic and quasiperiodic solutions. The approach is applicable to studying the dynamics of general forced nonsmooth oscillators of Hamiltonian type.