The Lyapunov exponent of holomorphic maps

Genadi Levin*, Feliks Przytycki, Weixiao Shen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We prove that for any polynomial map with a single critical point its lower Lyapunov exponent at the critical value is negative if and only if the map has an attracting cycle. Similar statement holds for the exponential maps and some other complex dynamical systems. We prove further that for the unicritical polynomials with positive area Julia sets almost every point of the Julia set has zero Lyapunov exponent. Part of this statement generalizes as follows: every point with positive upper Lyapunov exponent in the Julia set of an arbitrary polynomial is not a Lebegue density point.

Original languageAmerican English
Pages (from-to)363-382
Number of pages20
JournalInventiones Mathematicae
Issue number2
StatePublished - 1 Aug 2016

Bibliographical note

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© 2015, Springer-Verlag Berlin Heidelberg.


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