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

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

2002-06-10

arxiv.org/abs/math/0206105v1

Mathematics

Number Theory

58 pages, 15 figures

Scientific paper

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.

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