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Dynamics of the family \(\lambda \tan z\). (English) Zbl 0884.30019
Summary: We study the the tangent family \({\mathcal F} = \{\lambda \tan z, \lambda \in{\mathbb{C}}-\{0\}\}\) and give a complete classification of their stable behavior. We also characterize the hyperbolic components and give a combinatorial description of their deployment in the parameter plane.

MSC:
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
37F99 Dynamical systems over complex numbers
37B99 Topological dynamics
32H50 Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables
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