A Dual Approach to Triangle Sequences: A Multidimensional Continued Fraction Algorithm
Number Theory
2007-05-23 v1
Abstract
A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the triangle sequence. We give a new criterion for when a triangle sequence uniquely describes a pair of numbers and give the first explicit examples of triangle sequences that do not uniquely describe a pair of reals. Finally, this dual approach yields that the triangle sequence is topologically strongly mixing, meaning in particular that it is topologically ergodic.
Cite
@article{arxiv.math/0206105,
title = {A Dual Approach to Triangle Sequences: A Multidimensional Continued Fraction Algorithm},
author = {S. Assaf and L. Chen and T. Cheslack-Postava and B. Cooper and A. Diesl and T. Garrity and M. Lepinski and A. Schuyler},
journal= {arXiv preprint arXiv:math/0206105},
year = {2007}
}
Comments
58 pages, 15 figures