ON THE APPLICATION OF KAM THEORY TO DISCONTINUOUS DYNAMICAL-SYSTEMS

So Far the application of Kolmogorov-Arnold-Moser (KAM) theory has bee n restricted to smooth dynamical systems. Since there are many situati ons which can be modeled only by differential equations containing dis continuous terms such as state-dependent jumps (e.g., in control theor y or nonlinear oscillators), it is shown by a series of transformation s how KAM theory can be used to analyze the dynamical behaviour of suc h discontinuous systems as well. The analysis is carried out for the e xample (x) double over dot + x + a sgn(x) = p(t) with p is an element of C-6 being periodic. It is known that all solutions are unbounded fo r small a > 0. We prove that all solutions are bounded for a > 0 suffi ciently large, and that there are infinitely many periodic and quasipe riodic solutions in this case. (C) 1997 Academic Press.