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The nonconjugacy of certain exponential functions

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Holomorphic Functions and Moduli I

Part of the book series: Mathematical Sciences Research Institute Publications ((MSRI,volume 10))

Abstract

The exponential family Eλ(z) = λ exp z where λ is a nonzero complex number has been studied extensively (see [D], [DK], [DG], [DGH]). It is known that either

  • The stable set of Ωλ of Eλ consists of a single periodic cycle of stable regions and their preimages [GK], or

  • Ωλ = Ø.

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References

  1. Devaney, R., The structural instability of exp (z), Proc. AMS 94 (1985), 545–548.

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  2. Devaney, R. and Goldberg, L.R., Uniformization of attracting basins for exponential maps, Duke Journal (to appear).

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  3. Devaney, R., Goldberg, L.R. and Hubbard, J.H., A dynamical approximation to the exponential map by polynomials, to appear.

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  4. Devaney, R. and Krych, M., Dynamics of exp (z), Ergodic Theory and Dynamical Systems 4 (1984), 35–52.

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  5. Goldberg, L.R. and Keen, L., A Finiteness Theorem for a Dynamical Class of Entire Functions, Ergodic Theory and Dynamical Systems 6 (1986), 183–192.

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  6. Misiurewicz, M., On iterates of ez, Ergodic Theory and Dynamical Systems 1 (1981), 103–106.

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Author information

Authors and Affiliations

  1. Ecole Normale Superieure, USA

    Adrien Douady

  2. Brooklyn College, CUNY, USA

    Lisa R. Goldberg

Authors
  1. Adrien Douady
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  2. Lisa R. Goldberg
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Purdue University, West Layfayete, IN, 47909, USA

    D. Drasin

  2. Department of Mathematics, State University of New York at Stony Brook, Stony Brook, NY, 11794, USA

    I. Kra

  3. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    C. J. Earle

  4. Department of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    A. Marden

  5. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    F. W. Gehring

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© 1988 Springer-Verlag New York Inc.

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Cite this paper

Douady, A., Goldberg, L.R. (1988). The nonconjugacy of certain exponential functions. In: Drasin, D., Kra, I., Earle, C.J., Marden, A., Gehring, F.W. (eds) Holomorphic Functions and Moduli I. Mathematical Sciences Research Institute Publications, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9602-4_1

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  • DOI: https://doi.org/10.1007/978-1-4613-9602-4_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9604-8

  • Online ISBN: 978-1-4613-9602-4

  • eBook Packages: Springer Book Archive

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