Lecture Notes in Mathematics Volume 1342, 1988, pp 105-111
Date: 28 Sep 2006

Dynamics of tangent

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Abstract

We discuss the dynamics of the family of meromorphic maps z→λ tan z. The Julia sets of these maps have several interesting properties which are strikingly different from those of rational maps. For example, the Julia set is a smooth submanifold of the plane for every λ>1; for families of rational maps, those whose Julia sets are smooth submanifolds are isolated points.