Invariant algebraic curves of large degree for quadratic system

Colin Christopher, Jaume Llibre, Grzegorz Świrszcz

Research output: Contribution to journalArticleResearchpeer-review

18 Citations (Scopus)

Abstract

In this paper we present for the first time examples of algebraic limit cycles and saddle loops of degree greater than 4 for planar quadratic systems. In particular, we give examples of algebraic limit cycles of degree 5 and 6, and algebraic saddle loops of degree 3 and 5 surrounding a strong focus. We also give an example of an invariant algebraic curve of degree 12 for which the quadratic system has no Darboux integrating factors or first integrals. © 2004 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)450-461
JournalJournal of Mathematical Analysis and Applications
Volume303
DOIs
Publication statusPublished - 15 Mar 2005

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