Work

A new mechanism for producing degenerate centers in polynomial differential systems

Year: 2025

Type: article

Abstract: It has been conjectured that the only mechanisms capable of producing a center – whether degenerate or not – at a singular point of a polynomial differential system are algebraic reducibility and Liouvillian integrability. In this work, we present an example that is algebraically reducible but neither orbitally reversible nor Liouvillian integrable. The construction of this example is based on a recently developed mechanism that establishes a necessary and sufficient condition for the existence of a center.

Source: Nonlinear Analysis

DOI: 10.1016/j.na.2025.113981

Authors: Jaume Giné, Dmitry I. Sinelshchikov

Institutions: Universitat de Lleida, Ikerbasque, University of the Basque Country, Instituto Biofisika

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: $2,690