Paper
On a tree of rational functions related to continued fractions
Authors
Niels Langeveld, David Ralston
Abstract
In this article, we present a binary tree with vertices given by rational functions ; the root and functional derivation of children are inspired by continued fractions. We prove some special properties of the tree. For example, the zero solutions of the denominators are all real negative numbers and are dense in . For functions are non intersecting and form a dense subset of . Furthermore, when evaluating the tree for positive rational values, the tree contains every rational in exactly once if and only if . For , one finds back the classical Farey tree which is related to regular continued fractions. In the last part, we will make a similar tree in a similar way but for backward continued fractions. We highlight some similarities and differences.