Convergence of improper Iwasawa Continued Fractions
Number Theory
2022-05-26 v1
Abstract
We prove the convergence of a wide class of continued fractions, including generalized continued fractions over quaternions and octonions. Fractional points in these systems are not bounded away from the unit sphere, so that the iteration map is not uniformly expanding. We bypass this problem by analyzing digit sequences for points that converge to the unit sphere under iteration, expanding on previous methods of Dani-Nogueira.
Keywords
Cite
@article{arxiv.2205.12801,
title = {Convergence of improper Iwasawa Continued Fractions},
author = {Anton Lukyanenko and Joseph Vandehey},
journal= {arXiv preprint arXiv:2205.12801},
year = {2022}
}
Comments
23 pages, 3 figures