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Desingularization Theory and Bifurcation of Non-elementary Limit Periodic Sets

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Bifurcation of Planar Vector Fields and Hilbert’s Sixteenth Problem

Part of the book series: Modern Birkhäuser Classics ((MBC,volume 164))

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Abstract

In the study of the Bogdanov-Takens unfolding, we introduced in 4.3.5.2 the following formulas of rescaling in the phase-space and in the parameter space:

$$ x = {r^2}\bar x,y = {r^3}\bar y,\mu = - {r^4},\nu = {r^2}\bar \nu . $$

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© 1998 Springer Basel AG

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Roussarie, R. (1998). Desingularization Theory and Bifurcation of Non-elementary Limit Periodic Sets. In: Bifurcation of Planar Vector Fields and Hilbert’s Sixteenth Problem. Modern Birkhäuser Classics, vol 164. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8798-4_6

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  • DOI: https://doi.org/10.1007/978-3-0348-8798-4_6

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9778-5

  • Online ISBN: 978-3-0348-8798-4

  • eBook Packages: Springer Book Archive

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