A Topological–Analytical Method for Proving Averaging Theorems on an Infinite Time Interval in a Degenerate Case

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Steklov Institute of Mathematics Pub Date : 2023-12-20 DOI:10.1134/s0081543823040168

Ivan Yu. Polekhin

引用次数: 0

Abstract

We present a topological–analytical method for proving some results of the N. N. Bogolyubov averaging method for the case of an infinite time interval. The essence of the method is to combine topological methods of proving the existence of a periodic solution applied to the averaged system with Bogolyubov’s theorem on the averaging on a finite time interval. The proposed approach allows us to dispense with the nondegeneracy condition for the Jacobi matrix from the classical theorems of the averaging method.

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在退化情况下证明无限时间间隔上平均定理的拓扑分析方法

摘要我们提出了一种拓扑分析方法，用于证明 N. N. Bogolyubov 平均法在无限时间间隔情况下的一些结果。该方法的实质是将证明周期解存在的拓扑方法与博格留波夫关于有限时间间隔上的平均定理结合起来。所提出的方法使我们可以省去平均法经典定理中雅各比矩阵的非退化条件。

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

Proceedings of the Steklov Institute of Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

20.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Proceedings of the Steklov Institute of Mathematics is a cover-to-cover translation of the Trudy Matematicheskogo Instituta imeni V.A. Steklova of the Russian Academy of Sciences. Each issue ordinarily contains either one book-length article or a collection of articles pertaining to the same topic.