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Limit cycle bifurcations from a nilpotent focus or center of planar systems. (English) Zbl 1261.34032
Summary: We study analytic properties of the Poincaré return map and generalized focal values of analytic planar systems with a nilpotent focus or center. We use the focal values and the map to study the number of limit cycles of this class of systems and obtain some new results on the lower and upper bounds of the maximal number of limit cycles bifurcating from the nilpotent focus or center. The main results generalize the classical Hopf bifurcation theory and establish a new bifurcation theory for the nilpotent case.

MSC:
34C05Location of integral curves, singular points, limit cycles (ODE)
34C25Periodic solutions of ODE
34C23Bifurcation (ODE)
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References:
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