Chapter

Dynamical Systems

Volume 1342 of the series Lecture Notes in Mathematics pp 105-111

Date:

Dynamics of tangent

  • Robert L. DevaneyAffiliated withDepartment of Mathematics, Boston University
  • , Linda KeenAffiliated withDepartment of Mathematics, Herbert H. Lehman College, CUNY

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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.