%0 Journal Article
%T A proof of Perko's conjectures for the Bogdanov-Takens system
%A Armengol Gasull
%A Hector Giacomini
%A Set Perez-Gonzalez
%A Joan Torregrosa
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1303.2065v1