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On third-order nilpotent critical points: integral factor method. (English) Zbl 1248.34048
Summary: For third-order nilpotent critical points of a planar dynamical system, the problem of characterizing its center and focus is completely solved in this article by using the integral factor method. The associated quasi-Lyapunov constants are defined and their computation method is given. For a class of cubic systems under small perturbations, it is proved that there exist eight small-amplitude limit cycles created from a nilpotent critical point.

MSC:
34C23Bifurcation (ODE)
34C05Location of integral curves, singular points, limit cycles (ODE)
34C25Periodic solutions of ODE
34C07Theory of limit cycles of polynomial and analytic vector fields
34A05Methods of solution of ODE
34C45Invariant manifolds (ODE)
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