This paper summarizes, clarifies, and corrects some aspects of the variational velocity method for the detection of limit cycles. After definitions and statement of the most important theorems associated with this method, some aspects of the proof of the main theorem are corrected and reworked. An example from the original paper in Acta Appl. Math. 48 (1997), 13-32, is then discussed and criticized. Finally, the limitations of this method are discussed, especially as it applies to systems involving multiple limit cycles (and therefore as it applies to Hilbert's XVIth Problem).
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