非平凡各向同性群轨道的对称李雅普诺夫中心定理

IF 1.5 3区数学 Q1 MATHEMATICS

Advances in Differential Equations Pub Date : 2018-10-22 DOI:10.57262/ade/1580958057

Marta Kowalczyk, Ernesto P'erez-Chavela, S. Rybicki

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引用次数: 1

摘要

本文证明了对称势的李亚普诺夫中心定理的两个版本。我们考虑一个~二阶自治系统$\ddot q（t）=-\nabla U（q（t我们在潜在$U的临界点轨道的~邻域中寻找该系统的非平稳周期解$

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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Symmetric Lyapunov center theorem for orbit with nontrivial isotropy group

In this article we prove two versions of the Liapunov center theorem for symmetric potentials. We consider a~second order autonomous system $\ddot q(t)=-\nabla U(q(t))$ in the presence of symmetries of a compact Lie group $\Gamma$ acting linearly on $\mathbb{R}^n.$ We look for non-stationary periodic solutions of this system in a~neighborhood of an orbit of critical points of the potential $U.$

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来源期刊

Advances in Differential Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Differential Equations will publish carefully selected, longer research papers on mathematical aspects of differential equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new and non-trivial. Emphasis will be placed on papers that are judged to be specially timely, and of interest to a substantial number of mathematicians working in this area.