On the uniqueness problem for a central invariant manifold

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-07-27 DOI:10.1134/S0040577924070055

A. N. Kulikov

引用次数: 0

Abstract

We consider a system of autonomous nonlinear ordinary differential equations for which the existence conditions for an invariant manifold are satisfied in the case where this manifold is central. It is well known that the theorem on the existence of a central invariant manifold cannot be supplemented with the statement of its uniqueness. We obtain sufficient conditions that guarantee the uniqueness of the central invariant manifold.

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关于中心不变流形的唯一性问题

摘要我们考虑了一个自治非线性常微分方程系，在该方程系中，一个不变流形的存在条件在该流形是中心流形的情况下得到满足。众所周知，关于中心不变流形存在性的定理不能用其唯一性来补充说明。我们得到了保证中心不变流形唯一性的充分条件。

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

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.