Global dynamics of Newton's method for complex polynomials [ Back ]

Date:
02.07.20   
Times:
16:00 to 16:30
Place:
on-line
Speaker:
Martí Pedemonte
University:
Universitat de Barcelona

Abstract

 

The main goal of this talk is to understand and prove, using recently developed techniques,
Shishikura’s result on the connectivity of the Julia set of the Newton map of polynomials.
To do so, we first present a set of preliminary tools that contain normal families, conformal
representations and proper maps, among others. It is followed by a study of rational complex
dynamical systems, some results on the existence of fixed points of meromorphic maps and
it is concluded by what is the cornerstone of this project: the proof of the connectivity of the
Julia set of Newton maps of polynomials.