Work

Complete solution to the weak persistent center and isochronous center problems of cubic polynomial systems

Year: 2026

Type: preprint

Abstract: In this paper, we investigate weakly persistent centers for several classes of planar cubic differential systems, including systems with a nondegenerate linear center and systems with a nilpotent center. Necessary parameter relations are obtained by computing singular point quantities or quasi-Lyapunov constants, while their sufficiency is established by suitable analytic constructions. For the general complex cubic system, we obtain necessary and sufficient conditions for the origin to be a weakly persistent center, and the corresponding result for the associated general real cubic system follows by imposing the conjugacy relations between the complex coefficients. We further characterize the weakly persistent isochronous centers of the general complex cubic system by combining the weakly persistent center conditions with the vanishing of the linearization quantities and constructing time-preserving analytic linearizations.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.39761

Authors: Li, Feng, Liu, Huimei, Cao, Chen, Yu, Pei

Institutions: Linyi University, Shanghai Jiao Tong University, Western University

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Shandong Province

Awards: G1299771763, G7681730333

OpenAlex ID: W7215103269

Cites: 19

Cited by:

Related to: 10