Published June 8, 2005
| Version v1
Journal article
Open
A Dual Approach to Triangle Sequences: A Multidimensional Continued Fraction Algorithm
Authors/Creators
- 1. University of Notre Dame
- 2. Harvard University
- 3. Williams College
- 4. Johns Hopkins University
- 5. Department of Mathematics, Williams College, Williamstown, MA 01267
- 6. Rose-Hulman Institute of Technology
Description
A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in [9]) 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.