The focus-centre problem for a type of degenerate system

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Abstract

We consider differential systems in the plane defined by the sum of two homogeneous vector fields. We assume that the origin is a degenerate singular point for these differential systems. We characterize when the singular point is of focus-centre type in a generic case. The problem of its local stability is also considered. We compute the first generalized Lyapunov constant when some non-degeneracy conditions are assumed.
Original languageEnglish
Pages (from-to)699-729
JournalNonlinearity
Volume13
DOIs
Publication statusPublished - 1 May 2000

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