Reidemeister theory of iterations of endomorphisms and poly-Bieberbach groups

TL;DR

This paper develops a Reidemeister theory for iterated endomorphisms of poly-Bieberbach groups, analyzing the asymptotic behavior of Reidemeister numbers, periodic orbits, and heights to understand their algebraic and dynamical properties.

Contribution

It introduces a new Reidemeister theory for iterations of endomorphisms on poly-Bieberbach groups, exploring their asymptotic and dynamical features.

Findings

Analysis of the growth of Reidemeister numbers under iteration

Characterization of essential periodic orbits

Insights into the heights of endomorphisms on poly-Bieberbach groups

Abstract

We develop the Reidemeister theory of iterations of a group endomorphism $\varphi$ and study the asymptotic behavior of the sequence of the Reidemeister numbers of iterations $\{R(\varphi^k)\}$, the essential periodic $[\varphi]$-orbits and the heights of $\varphi$ on poly-Bieberbach groups.