Limit cycles for nonsmooth differential equations via Schwarzian derivative
type: Item
instance of: scholarly article
title: Limit cycles for nonsmooth differential equations via Schwarzian derivative
zbMATH Open document ID: 0901.34034
author: B. Coll
author: Armengol Gasull
author: Rafel Prohens
published in: Journal of Differential Equations
publication date: 1998-11-03T00:00:00Z
review text: Consider autonomous two-dimensional differential systems \[ dx/dt = P(x,y), \qquad dx/dt = Q(x,y) \tag \(*\) \] where \(P\) and \(Q\) are polynomials which can have a discontinuity at the \(x\)-axis. The authors study the maximal number of limit cycles of \((*)\). Under the assumption \(P\) and \(Q\) to be homogeneous polynomials satisfying some additional hypotheses, it is proved that \((*)\) possesses at most one singular limit cycle and two regular limit cycles where the number of the multiplicities of the regular cycles is not greater than two. A key point in the proof is the study of the Schwarzian derivative of the return map.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 1000160
zbMATH Keywords: limit cycles
zbMATH Keywords: Schwarzian derivative
zbMATH Keywords: nonsmooth differential equations
MaRDI profile type: Publication
full work available at URL: jdeq.1996.0177
OpenAlex ID: W2075445445
DOI: 10.1006/JDEQ.1996.0177
description: scientific article; zbMATH DE number 1000160