ABSTRACT

Recent progress in perturbation enables us to find many conditionally periodic motions in every nonlinear dynamical system which is close to an integrable system (see [1,2]. The stability of all the motions of the system follows from these results only when the dimension of the phase space is ≤ 4. The purpose of the present note is to give an example (3) of a system with a 5-dimensional phase space which satisfies all the conditions of [1,2] but is nonstable. * The secular changes I 2 in the system (3) have the velocity exp ( − 1 / ϵ ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003069515/f3ef54a9-ca7f-48a5-bad6-5d54427f48cf/content/eq4763.tif"/> and consequently cannot be dealt with by any approxi mation of the classical theory of perturbations.