Dynamics of Generalized Tangent-Like Maps

Abstract

For the class [Formula: see text] of meromorphic functions outside a compact countable set of essential singularities, we study the dynamics of some functions in [Formula: see text] for which the unit disc and its complement are invariant. These functions are products and compositions of the function [Formula: see text] with Blaschke products, that include the family [Formula: see text], which are the main topic of the article. Slices of the space of parameters of [Formula: see text] are given with a discussion of their main features. We construct a Poincaré extension of [Formula: see text] to the hyperbolic three-dimensional space and to the 3-sphere. Also we study their dynamics.