Work

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

Year: 2013

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1303.2065

Authors: Gasull, Armengol, Giacomini, Hector, Perez-Gonzalez, Set, Torregrosa, Joan

Institutions: Universitat Autònoma de Barcelona, Université de Tours, Centre National de la Recherche Scientifique, Laboratoire de Mathématiques et Physique Théorique

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Generalitat de Catalunya

Award: G4089352303

OpenAlex ID: W2951385115

Cites: 5

Cited by: 1

Related to: 20