Farey map, Diophantine approximation and Bruhat-Tits tree
Dynamical Systems
2014-01-24 v1 Group Theory
Number Theory
Abstract
Based on Broise-Alamichel and Paulin's work on the Gauss map corresponding to the principal convergents, we continue the study of the Gauss map via Farey maps to contain all the intermediate convergents. We define the geometric Farey map, which is given by time-1 map of the geodesic flow. We also define algebraic Farey maps, better suited for arithmetic properties, which produce all the intermediate convergents. Then we obtain the ergodic invariant measures for the Farey maps and the convergent speed.
Cite
@article{arxiv.1401.5866,
title = {Farey map, Diophantine approximation and Bruhat-Tits tree},
author = {Dong Han Kim and Seonhee Lim and Hitoshi Nakada and Rie Natsui},
journal= {arXiv preprint arXiv:1401.5866},
year = {2014}
}
Comments
19 pages, 2 figures