Bifurcations of Planar Vector Fields and Hilbert’s Sixteenth Problem

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r Presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. The text provides a systematic introduction to such methods as division of an analytic family of functions in its ideal of coefficients and asymptotic expansion of non-differentiable return maps and desingularisation. The exposision moves from classical analytic geometric methods to regular limit periodic sets to more recent tools for singular limit sets.