ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

On the Problem of Resolution of an Intricate Singularity for Three-dimensional System


M. R. Bortkovskaya

Saint-Petersburg State Technical University,
Department of High Mathematics,
Polytechnicheskaya st., 29, 195251, St.Petersburg, Russia


In the paper we consider a class of analytic three-dimensional systems with a singular point at the origin O(0,0,0). The linearized system at O is assumed to have a zero eigenvalue of multiplicity three. For O-curves we introduce the notions of vector curvature orders and vector curvature measures, and the concept of a regular O-curve. The problem under study is to resolve the singularity of a system at O relative to a given vector curvature order of O-curves, i.e. the problem is to find all regular O-curves with a given curvature order. Sufficient conditions of the resolution of singularity relative to a possible vector curvature order are obtained. These conditions appear through the analysis of Frommer's method used for finding possible vector curvature orders.

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