Limit cycles near hyperbolas in quadratic systems

Joan C. Artés, Freddy Dumortier, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

In this paper we introduce the notion of infinity strip and strip of hyperbolas as organizing centers of limit cycles in polynomial differential systems on the plane. We study a strip of hyperbolas occurring in some quadratic systems. We deal with the cyclicity of the degenerate graphics D I2 a from the programme, set up in [F. Dumortier, R. Roussarie, C. Rousseau, Hilbert's 16th problem for quadratic vector fields, J. Differential Equations 110 (1994) 86-133], to solve the finiteness part of Hilbert's 16th problem for quadratic systems. Techniques from geometric singular perturbation theory are combined with the use of the Bautin ideal. We also rely on the theory of Darboux integrability. © 2008 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)235-260
JournalJournal of Differential Equations
Volume246
DOIs
Publication statusPublished - 1 Jan 2009

Keywords

  • Limit cycle
  • Quadratic vector field
  • Strip of hyperbolas

Fingerprint

Dive into the research topics of 'Limit cycles near hyperbolas in quadratic systems'. Together they form a unique fingerprint.

Cite this