Holomorphic Functions and Moduli I

Volume 10 of the series Mathematical Sciences Research Institute Publications pp 9-30

Dynamics of holomorphic self-maps of ℂ*

  • Linda KeenAffiliated withDepartment of Mathematics, Herbert H. Lehman College, C.U.N.Y.

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In this paper we classify the stable components of holomorphic self-maps of ℂ* which have finitely many singular values. We use this to study a one and a two parameter family of such functions. We examine the dynamic dependence of these functions on the parameters and study the parameter spaces themselves.