Orbit counting in conjugacy classes for free groups acting on trees
Dynamical Systems
2016-07-01 v3 Group Theory
Abstract
In this paper we study the action of the fundamental group of a finite metric graph on its universal covering tree. We assume the graph is finite, connected and the degree of each vertex is at least three. Further, we assume an irrationality condition on the edge lengths. We obtain an asymptotic for the number of elements in a fixed conjugacy class for which the associated displacement of a given base vertex in the universal covering tree is at most . Under a mild extra assumption we also obtain a polynomial error term.
Cite
@article{arxiv.1502.02591,
title = {Orbit counting in conjugacy classes for free groups acting on trees},
author = {George Kenison and Richard Sharp},
journal= {arXiv preprint arXiv:1502.02591},
year = {2016}
}
Comments
13 pages, additional section discusses error terms, revised exposition