A proof of Perko's conjectures for the Bogdanov-Takens system
Dynamical Systems
2013-03-11 v1
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.
Keywords
Cite
@article{arxiv.1303.2065,
title = {A proof of Perko's conjectures for the Bogdanov-Takens system},
author = {Armengol Gasull and Hector Giacomini and Set Perez-Gonzalez and Joan Torregrosa},
journal= {arXiv preprint arXiv:1303.2065},
year = {2013}
}