Asymptotic decomposition of slow integral manifolds (Q1920843)

The authors consider a singularly perturbed system of differential equations \(\varepsilon \dot z = Z(z,t, \varepsilon)\) under the assumption that the limit system of equations \(Z(z,t,0) = 0\) \((\varepsilon = 0)\) admits an \(m\)-parametric family of solutions \(z = \psi (v,t)\), \(v \in \mathbb{R}^m\), \(t \in \mathbb{R}\), where \(\psi\) is a sufficiently smooth vector function. They investigate the question of existence of an integral manifold of slow motions (a ``slow integral manifold'') \(z = P(v,t, \varepsilon)\) on which the motion is gouverned by an equation \(\dot v = Q (v,t, \varepsilon)\). The authors present several methods for computing such manifolds in the form of asymptotic expansions in powers of the small parameter \(\varepsilon\), and they obtain some results on their stability.