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Higher order limit cycle bifurcations from non-degenerate centers. (English) Zbl 1255.34041

The paper is devoted to the computation of the Poincaré-Lyapunov constants and to the determination of their functionally independent number for the following systems \[ \dot{x}=-y+P_n(x, y), \;\dot{y}=x+Q_n(x, y), \] where \(P_n\) and \(Q_n\) are homogeneous polynomials of degree \(n\). By means of center bifurcation, the author estimates the cyclicity of a unique singular point of focus-center type for different values of \(n\). The presented results are obtained by using the implementation worked out by C. Christopher which exploits Cartesian coordinates and the computer algebra system Reduce.

MSC:

34C23 Bifurcation theory for ordinary differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C25 Periodic solutions to ordinary differential equations

Software:

strudel; REDUCE
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Full Text: DOI

References:

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