Multiplicities of limit cycles appearing after perturbations of hyperbolic polycycles

Pub Date : 2023-01-01 DOI:10.4213/sm9747e
A. Dukov
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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。
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