Work

Characterization of centers by their complex separatrices

Year: 2025

Type: article

Abstract: In this work, we address analytic families of real planar vector fields having a monodromic singularity at the origin for all parameters, where Λ is an open subset of the real finite-dimensional Euclidean space. We assume that depends analytically on λ. This naturally leads to the so-called center-focus problem, which consists of describing the partition of Λ induced by the centers and the foci at the origin. We provide a characterization of the centers (whether degenerate or not) in terms of a specific integral of the cofactor associated with a real invariant analytic curve passing through the singularity, which always exists. Several consequences and applications are also discussed.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2025.113506

Authors: Isaac A. García, Jaume Giné

Language: English

Topic: Advanced Differential Equations and Dynamical Systems

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: Agencia Nacional de Investigación y Desarrollo, Agència de Gestió d'Ajuts Universitaris i de Recerca, Agencia Estatal de Investigación

Awards: G3560423303, G4701358618