Non-isochronicity of the center in polynomial Hamiltonian systems |
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Authors: | Zhaoxia Wang |
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Affiliation: | Yangtze Center of Mathematics and Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, PR China |
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Abstract: | In 2002 Jarque and Villadelprat proved that planar polynomial Hamiltonian systems of degree 4 have no isochronous centers and raised an open question for general planar polynomial Hamiltonian systems of even degree. Recently, it was proved that a planar polynomial Hamiltonian system is non-isochronous if a quantity, denoted by M2m−2, can be computed such that M2m−2≤0. As a corollary of this criterion, the open question was answered for those systems with only even degree nonlinearities. In this paper we consider the case of M2m−2>0 and give a new criterion for non-isochronicity. Applying the new criterion, we also answer the open question for some cases in which some terms of odd degree are included. |
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Keywords: | 34C05 34C23 |
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