STABLE AND OSCILLATING MOTIONS IN NONAUTONOMOUS DYNAMICAL SYSTEMS. A GENERALIZATION OF C. L. SIEGEL'S THEOREM TO THE NONAUTONOMOUS CASE

Abstract

In this paper we generalize to the nonautonomous case a theorem of C. L. Siegel on the reducibility of an analytic dynamical system to normal form in a neighborhood of an equilibrium point. In fact, under certain concrete assumptions with respect to the behavior of the system as t→∞, we show that in a neighborhood of an equilibrium we can reduce the system to a linear system by means of a change of coordinates that depends on the time t and is analytic in the remaining variables. The results obtained are applicable to the problem of the stability of an equilibrium point. Bibliography: 16 items.