Integral manifolds for nonautonomous slow fast systems without dichotomy [Elektronische Ressource] / von Ekaterina Shchetinina

Integral Manifolds for NonautonomousSlow-Fast Systems without DichotomyDissertationzur Erlangung des akademisches Grades Doktor rer. nat.im Fach Mathematikeingereicht an derMathematisch-Naturwissenschaftlichen Fakult¨at IIHumboldt-Universit¨at zu BerlinvonFrau Dipl.-Math. Ekaterina Shchetininageb. am 09.04.1977 in Samara, RußlandPr¨asident/Pr¨asidentin der Humboldt-Universit¨at zu BerlinProf. Dr. Jurg¨ en MlynekDekan/Dekanin der Mathematisch-Naturwissenschaftlichen Fakult¨atProf. Dr. Uwe Kuc¨ hlerGutachter:1. Prof. Dr. Barbara Niethammer2. Priv.-Doz. Dr. Klaus R. Schneider3. Prof. Dr. Vladimir A. Soboleveigereicht am: 4.Mai 2004Tag der mundlic¨ hen Prufung:¨ 20. Juli 2004AbstractThis work is devoted to nonautonomous slow-fast systems of ordinarydifferential equation without dichotomy. We are interested in the existenceof a slow integral manifold in order to eliminate the fast variables.The peculiarity of the problem under consideration is that the righthand side of the system depends on some parameter vector which can beconsidered as a control to be determined in order to guarantee the existenceof an integral manifold consisting of canard trajectories. We call the vectorfunction as gluing function. We prove that under some conditions on theright hand side of the system there exists a unique gluing function suchthat the system has a slow integral manifold.