Iterations of the family ¿tanz²

Iterating a complex analytic map gives rise to a discrete conformal dynamical system. The theory of these dynamical systems was first introduced by Fatou and Julia in the 1920's. Interest in this subject has grown due to the graphics capabilities of computers and to the infusion of techniques from the theory of quasi-conformal mapping from the work of Sullivan, Douady, Hubbard, and many others. In [51], Devaney and Keen began the development of an iteration theory for meromorphic functions. They studied the class of meromorphic functions with polynomial Schwarzian derivatives. This book study the dynamics of a particular class of these meromorphic functions, the family F: z¿ ¿ tan z^2 where ¿ ¿ C ¿ {0}.