期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 380, 期 -, 页码 181-197出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2023.10.034
关键词
Critical periods; Hamiltonian vector fields; Best lower bound; Degree n vector field
类别
This paper provides the best lower bound for the number of critical periods of planar polynomial centers known up to now. The new lower bound is obtained in the Hamiltonian class and considering a single period annulus. The key idea is the perturbation of a vector field with many cusp equilibria, which is constructed using elements of catastrophe theory.
provide the best lower bound for the number of critical periods of planar polynomial centers known up to now. The new lower bound is obtained in the Hamiltonian class and considering a single period annulus. This lower bound doubles the previous one from the literature, and we end up with at least n2 - 2 (resp. n2 - 2n - 1) critical periods for planar polynomial systems of odd (resp. even) degree n. Key idea is the perturbation of a vector field with many cusp equilibria, whose construction is by itself a nontrivial construction that uses elements of catastrophe theory.(c) 2023 Elsevier Inc. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据