Ergodic Properties of Heisenberg Continued Fractions with Applications in Hyperbolic Geometry
arXiv:1610.09588
Abstract
We give an overview of how to construct continued fractions on the Heisenberg group , the projective and planar Siegel models of the group, and how to perform computations on the group using matrices. We discuss and work with some recent results of Vandehey on the classification of which elements of the Heisenberg group have eventually periodic continued fraction expansions.Then we examine and work with major theorems in ergodic theory to explore results concerning growth of denominators and digit frequency, relating the results to hyperbolic geometry.
arXiv comment14 pages, 4 figures. The majority of the first 11 pages were a part of an unpublished manuscript with another author, who has requested that I withdraw the paper at this time