From Abel's differential equations to Hilbert's 16th problem
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2024
Abstract:	The study of the limit cycles of planar polynomial differential equations is motivated both by its appearance in many mathematical models of the real-world as for the second part of Hilbert's 16th problem. In this work we briefly summarize some results on this subject and we will also highlight the important role that the Abel's differential equations play in its study. In the way, we recall some nice properties of the Riccati's differential equations.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00 Agencia Estatal de Investigación CEX2020-001084-M Agència de Gestió d'Ajuts Universitaris i de Recerca 2021/SGR-00113
Note:	Altres ajuts: acords transformatius de la UAB
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Polynomial diferential equation ; Periodic orbit ; Limit cycle ; Hilbert's 16 h problem ; Riccati's equation ; Abel's equation
Published in:	São Paulo Journal of Mathematical Sciences, Vol. 18, Issue 2 (December 2024) , p. 1342-1379, ISSN 2316-9028

DOI: 10.1007/s40863-024-00471-2

38 p, 2.4 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles