Algebraic Multiplicity and the Poincaré Problem

2023/09/28 by Lei, Jinzhi, Yang, Lijun
#34A05 #34M99 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.16392

Abstract

In this paper we derive an upper bound for the degree of the strict invariant algebraic curve of a polynomial system in the complex project plane under generic condition. The results are obtained through the algebraic multiplicities of the system at the singular points. A method for computing the algebraic multiplicity using Newton polygon is also presented.

Related

• The Poincaré problem for reducible curves
• Bi-Lipschitz invariance of the multiplicity
• Multiplicity estimates, analytic cycles and Newton polytopes
• Multiplicity of Invariant Algebraic Curves and Darboux Integrability
• A short survey on Newton polytopes, tropical geometry and ring of conditions of algebraic torus