Mathematische Zeitschrift

, Volume 288, Issue 3–4, pp 855–873 | Cite as

Lyapunov exponents and related concepts for entire functions

  • Walter Bergweiler
  • Xiao Yao
  • Jianhua Zheng


Let f be an entire function and denote by \(f^\#\) the spherical derivative of f and by \(f^n\) the n-th iterate of f. For an open set U intersecting the Julia set J(f), we consider how fast \(\sup _{z\in U} (f^n)^\#(z)\) and \(\int _U (f^n)^\#(z)^2 dx\,dy\) tend to \(\infty \). We also study the growth rate of the sequence \((f^n)^\#(z)\) for \(z\in J(f)\).

Mathematics Subject Classification

Primary 37F10 Secondary 30D05 



We thank Alexandre Eremenko, Dan Liu, Lasse Rempe-Gillen, Phil Rippon, Weixiao Shen and the referee for helpful comments.


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Copyright information

© Springer-Verlag GmbH Deutschland 2017

Authors and Affiliations

  1. 1.Mathematisches SeminarChristian-Albrechts-Universität zu KielKielGermany
  2. 2.Shanghai Center for Mathematical SciencesShanghaiPeople’s Republic of China
  3. 3.Department of Mathematical SciencesTsinghua UniversityBeijingPeople’s Republic of China

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