Orbit counting with an isometric direction
Dynamical Systems
2007-05-23 v1 Number Theory
Abstract
Analogues of the prime number theorem and Merten's theorem are well-known for dynamical systems with hyperbolic behaviour. In this paper a 3-adic extension of the circle doubling map is studied. The map has a 3-adic eigendirection in which it behaves like an isometry, and the loss of hyperbolicity leads to weaker asymptotic results on orbit counting than those obtained for hyperbolic maps.
Cite
@article{arxiv.math/0407166,
title = {Orbit counting with an isometric direction},
author = {G. Everest and V. Stangoe and T. Ward},
journal= {arXiv preprint arXiv:math/0407166},
year = {2007}
}