Limit Cycles and Invariant Algebraic Curves
Gasull, Armengol (Universitat Autònoma de Barcelona)
Santana, Paulo Henrique Reis (Universidade Estadual Paulista "Júlio de Mesquita Filho". Instituto de Biociências, Letras e Ciências Exatas)

Date:	2026
Abstract:	We give lower bounds in terms of n for the number of limit cycles of polynomial vector fields of degree n having any prescribed invariant algebraic curve. By applying them when the ovals of this curve are also algebraic limit cycles, we obtain a new recurrent property for the Hilbert numbers. Finally, we apply our results to two important families of models: Kolmogorov systems and a general family of systems appearing in game theory.
Grants:	Agencia Estatal de Investigación PID2022-136613NB-I00
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Hilbert 16th problem ; Limit cycles ; Invariant algebraic curves ; Kolmogorov systems ; Game theory models
Published in:	Communications on pure & applied analysis, Vol. 28 (April 2026) , p. 214-220, ISSN 1553-5258

DOI: 10.3934/cpaa.2026012

Postprint 7 p, 283.9 KB

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