Global Centers in a Class of Quintic Polynomial Differential System

2023/12/09 by Leonardo Pereira Costa da Cruz, Jaume Llibre, da Cruz, Leonardo P. C. +1
Engineering · Mathematics · Physics and Astronomy · #34C05 (Primary) #Advanced Differential Equations and Dynamical Systems #Control and Dynamics of Mobile Robots #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2312.05709

openalex publication_date 2023/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A center of a differential system in the plane ℝ² is an equilibrium point p having a neighborhood U such that U∖ \p\ is filled of periodic orbits. A center p is global when ℝ²∖ \p\ is filled of periodic orbits. In general is a difficult problem to distinguish the centers from the foci for a given class of differential systems, and also it is difficult to distinguish the global centers inside the centers. The goal of this paper is to classify the centers and the global centers of the following class of quintic polynomial differential systems x= y, y=-x+a₀₅ y⁵+a₁₄ x y⁴+a₂₃ x² y³+a₃₂ x³ y²+a₄₁ x⁴ y+a₅₀ x⁵, in the plane ℝ².

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