Ciclos límite en el plano: Contribuciones desde Chile: Limit cycles in the plane: Contributions from Chile

J. D. García-Saldaña; S. Rebollo-Perdomo

doi:10.56754/0719-0646.2702.391

DOI:

https://doi.org/10.56754/0719-0646.2702.391

Abstract

This article aims to highlight some important contributions made from Chile to the study of limit cycles of polynomial differential systems in the real plane, concerning the second half of Hilbert's sixteenth problem. This work is based on two main motivations: on the one hand, some of the results we analyze have not received the attention they deserve; and on the other hand, we expect renewed momentum in the coming decades in the study of limit cycles of polynomial differential systems. The results we present are situated within the international landscape, and we examine research challenges in this field.

Resumen

El objetivo de este artículo es destacar algunas contribuciones significativas realizadas desde Chile al estudio de ciclos límite en sistemas diferenciales polinomiales en el plano real, en relación con la segunda parte del problema 16 de Hilbert. Este trabajo se fundamenta en dos motivaciones principales: por una parte, algunos de los resultados analizados no han recibido la difusión que merecen; por otra, se anticipa un nuevo impulso en las próximas décadas en el estudio de los ciclos límite en sistemas diferenciales polinomiales. Los aportes presentados se sitúan dentro del panorama internacional y se examinan desafíos de investigación en este campo.

Keywords

Limit cycle , periodic orbit , differential system , Hilbert’s sixteenth problem

Mathematics Subject Classification:

34C07 , 34C08 , 34C25 , 37G15

J. D. García-Saldaña Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Concepción, Chile. https://orcid.org/0000-0002-4475-5064
S. Rebollo-Perdomo Departamento de Matemática, Universidad del Bío-Bío, Concepción, Chile. https://orcid.org/0000-0002-5526-9344

Pages: 391–410
Date Published: 2025-10-15
In Press

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