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arXiv · 1303.2065

A proof of Perko's conjectures for the Bogdanov-Takens system

Armengol Gasull·Hector Giacomini·Set Perez-Gonzalez·Joan Torregrosa
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Abstract

The Bogdanov-Takens system has at most one limit cycle and, in the parameter space, it exists between a Hopf and a saddle-loop bifurcation curves. The aim of this paper is to prove the Perko's conjectures about some analytic properties of the saddle-loop bifurcation curve. Moreover, we provide sharp piecewise algebraic upper and lower bounds for this curve.

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Armengol Gasull, Hector Giacomini, Set Perez-Gonzalez, Joan Torregrosa. 2013-03-08. A proof of Perko's conjectures for the Bogdanov-Takens system. https://arxiv.org/abs/1303.2065

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