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    Keen, Linda 1989. Topology and growth of a special class of holomorphic self-maps of *. Ergodic Theory and Dynamical Systems, Vol. 9, Issue. 02,

  • Ergodic Theory and Dynamical Systems, Volume 5, Issue 3
  • September 1985, pp. 329-335

On the measurable dynamics of zez

  • Etienne Ghys (a1), Lisa R. Goldberg (a2) and Dennis P. Sullivan (a3)
  • DOI:
  • Published online: 01 September 2008

We study the measure theoretic properties of the complex exponential map E(z) = ez.An particular, we show that the equivalence relation generated by E is recurrent and that E has no quasi-conformal deformations. This enables us to give some information concerning Devaney's semi-conjugacy between E and the shift map on sequences of integers.

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[4]L. Ahlfors & L. Bers . Riemann's mapping theorem for variable metrics. Annals of Math. 72, (1960), 385404.

[11]O. Lehto & K. I. Virtanen . Quasiconformal Mappings in the Plane. Springer-Verlag, 1973.

[13]E. H. Spanier . Algebraic Topology. McGraw-Hill, 1966.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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