2011/12/15 by Alastair N. Fletcher, Daniel A. Nicks, Fletcher, Alastair N. +1
Mathematics · #30C65 (Primary) 30D05 37F10 (Secondary) #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CV #math.DS #msc:30C65 #msc:30D05 #msc:37F10
paper · pdf · doi:10.48550/arxiv.1112.3589
24 pages, 3 figures
arxiv created 2011/12/15 · arxiv updated 2011/12/16
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.