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Generating limit cycles from a nilpotent critical point via normal forms. (English) Zbl 1100.34030

The authors develop a normal form theory which is applied to solve the center-focus problem for monodromic planar nilpotent singularities to generate limit cycles from this type of singularities.

MSC:

34C23 Bifurcation theory for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
37G05 Normal forms for dynamical systems
37G10 Bifurcations of singular points in dynamical systems
37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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