Dynamics of tangent

  • Robert L. Devaney
  • Linda Keen
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1342)


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.


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  1. [Bl]
    Blanchard, P. Complex Analytic Dynamics on the Riemann Sphere. BAMS (1984), 85–141.Google Scholar
  2. [Br]
    Brolin, H. Invariant Sets under Iteration of Rational Functions. Arkiv. für Matematik. 6 (1965), 103–144.MathSciNetCrossRefMATHGoogle Scholar
  3. [CGS]
    Curry, J., Garnett, L., and Sullivan, D. On the Iteration of a Rational Function. Comm. Math. Phys. 91 (1083), 267–277.MathSciNetCrossRefMATHGoogle Scholar
  4. [DK]
    Devaney, R. and Keen, L. Dynamics of Meromorphic Maps: Maps with Polynomial Schwarzian Derivatives. To appear.Google Scholar
  5. [DT]
    Devaney, R. and Tangerman, F. Dynamics of Entire Functions Near the Essential Singularity. Ergodic Theory and Dynamical Systems. 6 (1986), 489–503.MathSciNetCrossRefMATHGoogle Scholar
  6. [Ma]
    Mandelbrot, B. The Fractal Geometry of Nature. San Francisco: Freeman, 1982.MATHGoogle Scholar
  7. [Mi]
    Misiurewicz, M. On Iterates of e z. Ergodic Theory and Dynam. Sys. 1 (1981), 103–106.MathSciNetMATHGoogle Scholar
  8. [Mo]
    Moser, J. Stable and Random Motions in Dynamical Systems. Princeton: Princeton University Press, 1973.MATHGoogle Scholar
  9. [N]
    Nevanlinna, R. Uber Riemannsche Flächen mit endlich vielen Windungspunkten. Acta Math. 58 (1932).Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Robert L. Devaney
    • 1
  • Linda Keen
    • 2
  1. 1.Department of MathematicsBoston UniversityBoston
  2. 2.Department of MathematicsHerbert H. Lehman College, CUNYBronx

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