Xianbo Sun, Junmin Yang
Abstract:
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 |
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Junmin Yang College of Mathematics and Information Science Hebei Normal University Shijiazhuang, 050024 Hebei, China email:jmyzhw@sina.com |
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