Abstract
Levin, Przytycki and Shen [Invent. Math. 205 (2016), pp. 363–382] proved for a polynomial map f c ( z ) = z d + c f_c(z)=z^d+c , d ≥ 2 d\geq 2 and c ∈ C c \in \mathbb C , with Julia set J ( f ) J(f) of positive measure that for a.e. z ∈ J ( f ) z \in J(f) the Lyapunov exponent χ s ( z ) = 0 \chi _s(z)=0 . The aim of this paper is to show that the extension to non-entire transcendental meromorphic functions is not possible.
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