Asymptotics of solutions of systems with slow and fast variables (Q1067078)

The system (1) \(\dot x=\epsilon X(t,z,x,\epsilon)\), \(\dot z=Z(t,z,x,\epsilon)\) under investigation is replaced by a simpler one (2) \(\dot y=\epsilon Y(t,p,y)\), \(\dot p=P(t,p,y)\) close to (1) (in a sense defined by the author) and then sufficient conditions for the estimate \(\| x(t)-y(t)\| \leq \eta\), \(t\in (t_ 0,T(\epsilon))\) are given. Here x(t) and y(t) denote the ''slow'' components of solutions (x(t),z(t)), (y(t),p(t)) of (1) and (2) respectively. This generalizes similar previous results of the author [Dokl. Akad. Nauk SSSR 272, 315-319 (1983; Zbl 0554.34005)].