Study of the Complete Oscillation, Rotation, and Wandering Properties of a Differential System by the First Approximation

IF 0.6 4区数学 Q3 MATHEMATICS

Mathematical Notes Pub Date : 2024-07-05 DOI:10.1134/s0001434624030313

I. N. Sergeev

引用次数: 0

Abstract

The concepts of complete oscillation, rotation, and wandering as well as complete nonoscillation, nonrotation, and nonwandering of a system of differential equations (with respect to its zero solution) are introduced. A one-to-one relationship between these properties and the corresponding characteristics of the system is established. Signs of a guaranteed possibility of studying them using the first approximation system, as well as examples for which that is not possible, are given.

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用第一近似法研究微分系统的完全振荡、旋转和徘徊特性

摘要介绍了微分方程系统（关于其零解）的完全振荡、旋转和游走以及完全不振荡、不旋转和不游走的概念。这些性质与系统的相应特征之间建立了一一对应的关系。给出了使用第一近似系统研究这些特性的保证可能性的迹象，以及不可能使用第一近似系统的例子。

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

Mathematical Notes 数学-数学

CiteScore

0.90

自引率

16.70%

发文量

179

审稿时长

24 months

期刊介绍： Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.