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We propose a notion of Misiurewicz condition for transcendental entirefunctions and study perturbations of Speiser functions satisfying thiscondition in their parameter spaces (in the sense of Eremenko and Lyubich). Weshow that every Misiurewicz entire function can be approximated by hyperbolicmaps in the same parameter space. Moreover, Misiurewicz functions are Lebesguedensity points of hyperbolic maps if their Julia sets have zero Lebesguemeasure. We also prove that the set of Misiurewicz Speiser functions hasLebesgue measure zero in the parameter space.

Speiser meets Misiurewicz