Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 1999; 36(3): 459-467

Printed May 1, 1999

Copyright © The Korean Mathematical Society.

Bifurcation analysis on an unfolding of the Takens-Bogdanov singularity

Gil-Jun Han

Abstract

A complete analysis of the equation $x'=y,$ $y'=\beta y-\alpha x^2+\alpha^2x+\delta xy,$ where $\alpha$ and $ \beta$ small, describing a particular unfolding of the Takens-Bogdanov singularity is presented.

Keywords: center manifold reduction, normal form, unfolding, codimension, nilpotent singularity

MSC numbers: 34C05, 34C15, 34C23, 34D99

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