Lyapunov exponents and related concepts for entire functions
2018
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 \(z\in J(f)\).
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