A new mechanism for producing degenerate centers in polynomial differential systems

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.