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Estimate of the Number of Zeros of Abelian Integrals

Part of the Advanced Courses in Mathematics CRM Barcelona book series (ACMBIRK)

Abstract

To study the weak Hilbert’s 16th problem by using Abelian integrals, it is crucial to estimate the number of zeros of the Abelian integral. In this chapter, we introduce several methods to study the number of zeros of the Abelian integral I(h) given in (1.10), which is related to the codimension 2 Bogdanov-Takens bifurcation problem, as we explained in subsection 1.2.2.

Keywords

Rotation Number Bifurcation Problem Argument Principle Fuchsian System Abelian Integral 
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Copyright information

© Birkhäuser Verlag 2007

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