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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Parametric normal forms for Bogdanov--Takens singularity; the generalized saddle-node case

Pages: 205 - 224, Volume 35, Issue 1, January 2015      doi:10.3934/dcds.2015.35.205

 
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Majid Gazor - Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (email)
Mojtaba Moazeni - Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (email)

Abstract: We obtain a parametric (and an orbital) normal form for any non-degenerate perturbation of the generalized saddle-node case of Bogdanov--Takens singularity. Explicit formulas are derived and greatly simplified for an efficient implementation in any computer algebra system. A Maple program is prepared for an automatic parametric normal form computation. A section is devoted to present some practical formulas which avoid technical details of the paper.

Keywords:  Bogdanov--Takens singularity, generalized saddle-node, parametric normal form, orbital normal form, grading structures.
Mathematics Subject Classification:  Primary: 34C20; Secondary: 34A34, 16W50.

Received: May 2013;      Revised: June 2014;      Available Online: August 2014.

 References