Cyclicity of a class of polynomial nilpotent center singularities
Copyright policy )Cyclicity of a class of polynomial nilpotent center singularities
In this work we extend techniques based on computational algebra for bounding the cyclicity of nondegenerate centers to nilpotent centers in a natural class of polynomial systems, those of the form $\dot x = y + P_{2m + 1}(x,y)$, $\dot y = Q_{2m + 1}(x,y)$, where $P_{2m+1}$ and $Q_{2m+1}$ are homogeneous polynomials of degree $2m + 1$ in $x$ and $y$. We use the method to obtain an upper bound (which is sharp in this case) on the cyclicity of all centers in the cubic family and all centers in a broad subclass in the quintic family. The first author is partially supported by a MICINN grant number MTM2011-22877 and by a CIRIT grant number 2014 SGR 1204.
Bifurcations of singular points in dynamical systems, Nilpotent center, nilpotent center, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Limit cycle, cyclicity, limit cycle, Bifurcations of limit cycles and periodic orbits in dynamical systems, Cyclicity, Matemàtica, Mathematics
Bifurcations of singular points in dynamical systems, Nilpotent center, nilpotent center, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Limit cycle, cyclicity, limit cycle, Bifurcations of limit cycles and periodic orbits in dynamical systems, Cyclicity, Matemàtica, Mathematics
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