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Sbornik Mathematics
Article . 2023 . Peer-reviewed
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Multiplicities of limit cycles appearing after perturbations of hyperbolic polycycles

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2023 English Publisher:Steklov Mathematical InstituteJournal:Sbornik: Mathematics, volume 214, pages 226-245 (issn: 1064-5616, eissn: 1468-4802, Copyright policy )
Authors: Andrei Valerevich Dukov;

doi: 10.4213/sm9747e

Multiplicities of limit cycles appearing after perturbations of hyperbolic polycycles

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
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