On the topological entropy of families of braids

TL;DR

This paper introduces a method to compute the topological entropy of braids within infinite families using Dynnikov's coordinates, demonstrated on two specific two-parameter braid families.

Contribution

The paper presents a novel approach leveraging Dynnikov's coordinates to efficiently calculate topological entropy for entire braid families.

Findings

Method successfully computes entropy for infinite braid families

Illustrated on two two-parameter braid families

Provides a practical tool for analyzing braid complexity

Abstract

A method for computing the topological entropy of each braid in an infinite family, making use of Dynnikov's coordinates on the boundary of Teichm\"uller space, is described. The method is illustrated on two two-parameter families of braids.