Schwarz maps associated with the triangle groups (2,4,4) and (2,3,6)

TL;DR

This paper investigates Schwarz maps linked to specific triangle groups, analyzing their properties and applying the results to mean iterations, thereby advancing understanding of monodromy groups and iterative processes.

Contribution

It introduces formulas for Schwarz maps associated with the (2,4,4) and (2,3,6) triangle groups and explores their applications to mean iterations.

Findings

Derived explicit formulas for Schwarz maps of the specified triangle groups.

Connected Schwarz maps to mean iteration processes.

Enhanced understanding of monodromy groups in complex analysis.

Abstract

We study the Schwarz maps with monodromy groups isomorphic to the triangle groups (2,4,4) and (2,3,6) and their inverses. We apply our formulas to the study of mean iterations.