Iteration of quasiregular tangent functions in three dimensions
arXiv:1112.3589
Abstract
We define a new quasiregular mapping T in three dimensions that generalizes the tangent function on the complex plane and shares a number of its geometric properties. We investigate the dynamics of the family λT for λ>0, establishing results analogous to those of Devaney and Keen for the meromorphic family λtan z, λ>0, although the methods used are necessarily original.
24 pages, 3 figures