Electron. J. Diff. Equ., Vol. 2014 (2014), No. 40, pp. 1-12.

Sharp bounds of the number of zeros of Abelian integrals with parameters

Xianbo Sun, Junmin Yang

In this article, we study four Abelian integrals over compact level curves of four sixth-degree hyper-elliptic Hamiltonians with parameters. We prove that the sharp bound of the number of zeros for each Abelian integral is 2. The proofs rely mainly on the Chebyshev criterion for Abelian integrals and asymptotic expansions of Abelian integrals.

Submitted November 11, 2013. Published February 5, 2014.
Math Subject Classifications: 34C05, 34C07, 34C08.
Key Words: Limit cycle; Lienard system; Chebyshev system; bifurcation; heteroclinc loop.

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Xianbo Sun
Department of Applied Mathematics
Guangxi University of Finance and Economics
Nanning, 530003 Guangxi, China
email:xianbo01@126.com Tel +86 15977781786
Junmin Yang
College of Mathematics and Information Science
Hebei Normal University
Shijiazhuang, 050024 Hebei, China

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