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Analytic properties of the return mapping of Liénard equations. (English) Zbl 1032.34005

The author deals with analytic properties of the return mapping of Liénard equations used in many applications. The author develops a direct computation of the return mapping which yields an estimate on the domain of convergence by a majorizing series technique and a recurrence relation for the coefficients which entail the Bautin ideal.
Reviewer: Jihong Dou (Xian)

MSC:

34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
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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