Pseudodigits

Abstract

In a multidimensional radix representation, also known as a
positional number system, there may be some integer vectors with
periodic orbits under the transformation defined by the Euclidean
algorithm. For example, if we consider the integers base 2 with digits
0 and 1, then repeated applications of the Euclidean algorithm to any
negative integer will eventually fall into the orbit TeX Embedding failed!,
since TeX Embedding failed!. We choose a representative of each (nonzero)
periodic orbit, and define these representatives to be pseudodigits.
This talk will introduce some results on existence and properties of
periodic orbits and pseudodigits.

Details