A Dual Approach to Triangle Sequences: A Multidimensional Continued Fraction Algorithm

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
58 pages, 15 figures

Keywords

Number Theory, 11J70, 11K50, 11A55

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/64273

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0206105
 http://arxiv.org/abs/math/0206105

Collections

arXiv