Chebotarov continua, Jenkins-Strebel differentials and related problems: a numerical approach

TL;DR

This paper presents a numerical algorithm for constructing rational quadratic differentials on the Riemann sphere that satisfy the Boutroux condition, with applications to Chebotarov problems, Jenkins-Strebel differentials, and related areas.

Contribution

It introduces a novel numerical method and code for constructing Boutroux differentials with prescribed poles, advancing computational tools in complex analysis and related fields.

Findings

Successfully constructs Boutroux differentials with specific polar parts

Provides solutions to Chebotarov and Jenkins-Strebel problems

Enhances computational approaches in weighted capacity and Random Matrices

Abstract

We detail a numerical algorithm and related code to construct rational quadratic differentials on the Riemann sphere that satisfy the Boutroux condition. These differentials, in special cases, provide solutions of (generalized) Chebotarov problem as well as being instances of Jenkins--Strebel differentials. The algorithm allows to construct Boutroux differentials with prescribed polar part, thus being useful in the theory of weighted capacity and Random Matrices.