Asymptotic decomposition of slow integral manifolds
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.
scientific article; zbMATH DE number 917135
scientific article