Period function of planar turning points

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.14232/EJQTDE.2021.1.16

R. Huzak, D. Rojas

引用次数: 3

Abstract

This paper is devoted to the study of the period function of planar generic and non-generic turning points. In the generic case (resp. non-generic) a non-degenerate (resp. degenerate) center disappears in the limit e → 0, where e ≥ 0 is the singular perturbation parameter. We show that, for each e > 0 and e ∼ 0, the period function is monotonously increasing (resp. has exactly one minimum). The result is valid in an e-uniform neighborhood of the turning points. We also solve a part of the conjecture about a uniform upper bound for the number of critical periods inside classical Liénard systems of fixed degree, formulated by De Maesschalck and Dumortier in 2007. We use singular perturbation theory and the family blow-up.

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平面拐点的周期函数

本文主要研究平面一般拐点和非一般拐点的周期函数。在一般情况下(参见。非泛型的;非简并的;简并中心在极限e→0处消失，其中e≥0为奇异摄动参数。我们证明，对于每一个e > 0和e ~ 0，周期函数是单调递增的。只有一个最小值)。结果在拐点的e-均匀邻域内是有效的。我们还解决了De Maesschalck和Dumortier(2007)提出的经典定次lisamadard系统中临界周期数目一致上界的部分猜想。我们使用奇异摄动理论和家庭爆破。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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