A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems
type: Item
instance of: scholarly article
title: A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems
zbMATH Open document ID: 1481.34041
author: Jaume Llibre
author: Xiang Zhang
published in: Expositiones Mathematicae
publication date: 2021-06-25T00:00:00Z
review text: This work presents a survey dedicated to the algebraic and explicit non-algebraic limit cycles of polynomial differential systems in \(\mathbb{R}^2\) and of discontinuous piecewise differential systems formed by two linear differential systems separated by a straight line in \(\mathbb{R}^2\). For the polynomial differential systems the authors collect the most essential results related to the number and configurations of their algebraic limit cycles. Investigations of the algebraic and explicit non-algebraic limit cycles for the mentioned class of discontinuous piecewise differential systems is a new area of research. Therefore, only the first results derived in this area are mentioned in the presented survey. Additionally, the authors recall seven open problems devoted to these types of limit cycles.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34A36
zbMATH DE Number: 7363312
zbMATH Keywords: algebraic limit cycle
zbMATH Keywords: non-algebraic limit cycle
zbMATH Keywords: explicit limit cycle
zbMATH Keywords: polynomial differential system
zbMATH Keywords: piecewise linear differential system
MaRDI profile type: Publication
full work available at URL: j.exmath.2020.03.001
OpenAlex ID: W3036029400
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A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems (DOI)
DOI: 10.1016/J.EXMATH.2020.03.001