A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Zhang, X. (Shanghai Jiao Tong University. School of Mathematical Sciences and MOE-LSC (People's Republic of China))

Date:	2021
Abstract:	In the qualitative theory of differential equations in the plane one of the most difficult objects to study is the existence of limit cycles. There are many papers dedicated to this subject. Here we will present a survey mainly dedicated to the algebraic and explicit non-algebraic limit cycles of the polynomial differential systems in R and of the discontinuous piecewise differential systems in R formed by two linear differential systems separated by a straight line. For this class of discontinuous piecewise differential systems the study of their algebraic and explicit non-algebraic limit cycles just is starting. Here we provide the first explicit non-algebraic limit cycle for the discontinuous piecewise linear differential systems. Additionally we recall seven open questions related with these types of limit cycles.
Grants:	Ministerio de Ciencia e Innovación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Algebraic limit cycle ; Non-algebraic limit cycle ; Explicit limit cycle ; Polynomial differential system ; Piecewise linear differential system
Published in:	Expositiones Mathematicae, Vol. 39, Issue 1 (March 2021) , p. 48-61, ISSN 0723-0869

DOI: 10.1016/j.exmath.2020.03.001

Postprint 18 p, 798.2 KB

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