The bifurcation set of a rational function via Newton polytopes

2020/03/30 by Tat Thang Nguyen, Nguyen, Tat Thang, Takahiro Saito +3
Computer Science · Mathematics · #14F05 #14F43 #14M25 #32C38 #32S20 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2003.13308

openalex publication_date 2020/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The bifurcation sets of polynomial functions have been studied by many mathematicians from various points of view. In particular, Némethi and Zaharia described them in terms of Newton polytopes. In this paper, we will show analogous results for rational functions.

Related

• The bifurcation set of a real polynomial function of two variables and Newton polygons of singularities at infinity
• Quadratic and cubic Newton maps of rational functions
• Bifurcation values of polynomial functions and perverse sheaves
• Newton's method applied to rational functions: Fixed points and Julia sets
• Combinatorial properties of Newton maps