Free group automorphisms with parabolic boundary orbits

TL;DR

This paper demonstrates the existence of free group automorphisms with parabolic boundary orbits for ranks four and higher, providing a method to generate infinitely many such examples.

Contribution

It introduces a new technique for constructing free group automorphisms with parabolic boundary orbits, expanding understanding of their dynamics.

Findings

Existence of automorphisms with parabolic boundary orbits for N≥4

Development of a method to produce infinitely many such automorphisms

Contribution to the study of free group automorphism dynamics

Abstract

For $N\geq 4$, we show that there exist automorphisms of the free group $F_N$ which have a parabolic orbit in $\partial F_N$. In fact, we exhibit a technology for producing infinitely many such examples.