| The period function of potential systems of polynomials with real zeros | |
| Yang Lijun ; Zeng Xianwu | |
| 2010-10-12 ; 2010-10-12 | |
| 关键词 | Period function Period annulus Convexity Monotonicity Critical points REVERSIBLE QUADRATIC CENTERS LOTKA-VOLTERRA SYSTEM HAMILTONIAN-SYSTEMS CRITICAL-POINTS VECTOR-FIELDS BIFURCATION MONOTONICITY Mathematics, Applied |
| 中文摘要 | We consider some analytic behaviors (convexity, monotonicity and number of critical points) of the period function of period annuli of the potential system x + g(x) = 0 and focus on the case when g(x) is a polynomial whose roots are all real. The main contributions of this paper are twofold: (i) analytic behaviors are given for the period functions of period annuli surrounding one or more and simple or degenerate equilibria; (ii) as a nontrivial application of the general conclusions in (i), a purely analytical and shorter proof is provided for a result for the case deg g = 4 recently obtained by Chengzhi Li and Kening Lu with some help of computer algebra [Chengzhi Li, Kening Lu, The period function of hyperelliptic Hamiltonian of degree 5 with real critical points, Nonlinearity 21 (2008) 465-483]. (C) 2009 Elsevier Masson SAS. All rights reserved. |
| 语种 | 英语 ; 英语 |
| 出版者 | GAUTHIER-VILLARS/EDITIONS ELSEVIER ; PARIS ; 23 RUE LINOIS, 75015 PARIS, FRANCE |
| 内容类型 | 期刊论文 |
| 源URL | [http://hdl.handle.net/123456789/81229]  |
| 专题 | 清华大学 |
| 推荐引用方式 GB/T 7714 | Yang Lijun,Zeng Xianwu. The period function of potential systems of polynomials with real zeros[J],2010, 2010. |
| APA | Yang Lijun,&Zeng Xianwu.(2010).The period function of potential systems of polynomials with real zeros.. |
| MLA | Yang Lijun,et al."The period function of potential systems of polynomials with real zeros".(2010). |
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