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Dynamical Systems pp 105–111Cite as

Dynamics of tangent

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1342))

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.

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References

  1. Blanchard, P. Complex Analytic Dynamics on the Riemann Sphere. BAMS (1984), 85–141.

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  4. Devaney, R. and Keen, L. Dynamics of Meromorphic Maps: Maps with Polynomial Schwarzian Derivatives. To appear.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Boston University, 02215, Boston, Mass.

    Robert L. Devaney

  2. Department of Mathematics, Herbert H. Lehman College, CUNY, 10468, Bronx, N.Y.

    Linda Keen

Authors
  1. Robert L. Devaney
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  2. Linda Keen
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Editor information

James C. Alexander

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© 1988 Springer-Verlag

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Devaney, R.L., Keen, L. (1988). Dynamics of tangent. In: Alexander, J.C. (eds) Dynamical Systems. Lecture Notes in Mathematics, vol 1342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082826

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  • DOI: https://doi.org/10.1007/BFb0082826

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50174-9

  • Online ISBN: 978-3-540-45946-0

  • eBook Packages: Springer Book Archive

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