Multiplicities of limit cycles appearing after perturbations of hyperbolic polycycles

IF 0.8 4区数学 Q2 MATHEMATICS Sbornik Mathematics Pub Date : 2023-01-01 DOI:10.4213/sm9747e

A. Dukov

引用次数: 0

Abstract

The problem of the multiplicity of limit cycles appearing after a perturbation of a hyperbolic polycycle with generic set of characteristic numbers is considered. In particular, it is proved that the multiplicity of any limit cycle appearing after a perturbation in a smooth finite-parameter family does not exceed the number of separatrix connections forming the polycycle. Bibliography: 10 titles.

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双曲多环摄动后极限环的多重性

研究具有一般特征数集的双曲多环摄动后极限环的多重性问题。特别地，证明了在光滑有限参数族中，扰动后出现的任何极限环的多重性不超过形成该多环的分离矩阵连接数。参考书目:10篇。

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

Sbornik Mathematics 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. The journal has always maintained the highest scientific level in a wide area of mathematics with special attention to current developments in: Mathematical analysis Ordinary differential equations Partial differential equations Mathematical physics Geometry Algebra Functional analysis

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