Skip to main content
×
Home
    • Aa
    • Aa

On the measurable dynamics of zez

  • Etienne Ghys (a1), Lisa R. Goldberg (a2) and Dennis P. Sullivan (a3)
Abstract
Abstract

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.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      On the measurable dynamics of zez
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      On the measurable dynamics of zez
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      On the measurable dynamics of zez
      Available formats
      ×
Copyright
References
Hide All
[1]Ahlfors L. V.. Complex Analysis. McGraw Hill, 1966.
[2]Ahlfors L. V.. Lectures on Quasiconformal Mappings. D. Van Nostrand Company, Inc., 1966.
[3]Ahlfors L. V.. Conformal Invariants, Topics in Geometric Function Theory. McGraw Hill, 1973.
[4]Ahlfors L. & Bers L.. Riemann's mapping theorem for variable metrics. Annals of Math. 72, (1960), 385404.
[5]Devaney R.. Structural instability of Exp(z). To appear.
[6]Devaney R. & Krych. Dynamics of Exp (z). Ergod. Th. Dynam. Syst. 4, (1984), 3552.
[7]Fatou P.. Mémoire sur les equations fonctionnelles. B.S.M.F. 47, (1919), 161271; 47 (1920), 33–94 and 208–314.
[8]Fatou P.. Sur l'iteration des fonctions transcendantes entières. Ada Math. 47, (1926), 337370.
[9]Halmos P.. Ergodic Theory.
[10]Julia G.. Itération des applications fonctionelles. J. Math. Pures et Appl., (1918), 47245.
[11]Lehto O. & Virtanen K. I.. Quasiconformal Mappings in the Plane. Springer-Verlag, 1973.
[12]Misiurewicz M.. On iterates of e z. Ergod. Th. & Dynam. Syst. 1, (1981), 103106.
[13]Spanier E. H.. Algebraic Topology. McGraw-Hill, 1966.
[14]Sullivan D.. Quasiconformal homeomorphisms and dynamics, I. To appear.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 15 *
Loading metrics...

Abstract views

Total abstract views: 30 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd October 2017. This data will be updated every 24 hours.