Limit cycles of the classical Liénard differential systems: A survey on the Lins Neto, de Melo and Pugh's conjecture

Jaume Llibre, Xiang Zhang

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

© 2016 Elsevier GmbH In 1977 Lins Neto et al. (1977) conjectured that the classical Liénard system ẋ=y−F(x),ẏ=−x with F(x) a real polynomial of degree n, has at most [(n−1)/2] limit cycles, where [⋅] denotes the integer part function. In this paper we summarize what is known and what is still open on this conjecture. For the known results on this conjecture we present a complete proof.
Original languageEnglish
Pages (from-to)286-299
JournalExpositiones Mathematicae
Volume35
Issue number3
DOIs
Publication statusPublished - 1 Sep 2017

Keywords

  • Conjecture of Lins Neto, de Melo and Pugh
  • Limit cycle
  • Liénard system

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