"Simple Dynamics" conjectures for some real Newton maps on the plane

2018/12/01 by R. De Leo, De Leo, Roberto
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1812.00270

openalex publication_date 2018/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We collect from several sources some of the most important results on the forward and backward limits of points under real and complex rational functions, and in particular real and complex Newton maps, and we provide numerical evidence that a fundamental result by B.Barna on the dynamics of Newton's method on the real line extends to the real plane.

Citations

• An Experimental View of Herman Rings for Dianalytic Maps of \mathbbRP²

Related

• Julia sets of Newton maps of real quadratic polynomial maps on the plane
• Quadratic and cubic Newton maps of rational functions
• Rigidity of Newton dynamics
• Newton's method applied to rational functions: Fixed points and Julia sets
• A classification of postcritically finite Newton maps