Global centers of a class of cubic polynomial differential systems

2023/10/11 by Llibre, Jaume, Rondón, Gabriel
#34C05 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.07454

Abstract

A difficult classical problem in the qualitative theory of differential systems in the plane ℝ² is the center-focus problem, i.e. to distinguish between a focus and a center. Another difficult problem is to distinguish inside a family of centers the ones which are global. A global center is a center p such that ℝ²∖\p\ is filled with periodic orbits. In this paper we classify the global centers of the family of real polynomial differential systems of degree 3 that in complex notation write iw=w-A₃w²-A₄w³-A₅w²w-A₆ww², where w=x+iy and A_k∈ℂ for k=3,4,5,6.

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