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Isochronicity problem of a higher-order singular point for polynomial differential systems. (English) Zbl 1198.34048

The paper is devoted to the isochronicity problem of a higher-order singular point for a planar polynomial autonomous system. By applying a new recursive algorithm to compute period constants, the authors study this problem for the following real septic system \[ \begin{aligned} \frac{dx}{dt}&=-y(x^2 + y^2)+ \sum_{k+j=5}A_{kj}x^ky^j -\lambda y(x^2 + y^2)^3, \\ \frac{dy}{dt}&=x(x^2 + y^2)+ \sum_{k+j=5}B_{kj}x^ky^j +\lambda x(x^2 + y^2)^3. \end{aligned} \]

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations

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References:

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