Lyapunov exponents and related concepts for entire functions

Abstract

Let $f$ be an entire function and denote by $f^{\#}$ be 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 ${\int }_U(f^n{)}^{\#}(z{)}^{2}dxdy$ tend to $\infty$. We also study the growth rate of the sequence $(f^n{)}^{\#}(z)$ for $z\in J(f)$.

arXiv comment20 pages

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Cited by in corpus (2)

• Radially distributed values and normal families
• On the multipliers of repelling periodic points of entire functions