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

2013/03/08 by Armengol Gasull, Hector Giacomini, Héctor Giacomini +7 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:34C05 #msc:34C07 #msc:34C37 #msc:37G15

paper · pdf · doi:10.48550/arxiv.1303.2065

arxiv created 2013/03/08 · arxiv updated 2013/03/11

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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