We study colorings of a tree induced from isometries of the hyperbolic plane given an ideal tessellation. We show that, for a given tessellation of the hyperbolic plane by ideal polygons, a coloring can be associated with any element of Isom(), and the element is a commensurator of if and only if its associated coloring is periodic, generalizing a result of Hedlund and Morse.
"Hyperbolic Tessellation and Colorings of Trees." Abstr. Appl. Anal. 2013 (SI20) 1 - 6, 2013. https://doi.org/10.1155/2013/706496