Geometrically finite transcendental entire functions

For polynomials, local connectivity of Julia sets is a much-studied and important property. Indeed, when the set polynomial degree $d\geq 2$ locally connected, topological dynamics can be completely described as quotient much simpler system: angle $d$-tupling on circle. transcendental entire function, less significant, but we may still ask for description system. To this end, introduce notion "docile" functions: function with bounded postsingular docile if it suitable disjoint-type function. Moreover, prove docility large class geometrically finite functions criticality set. This seen an analogue first proved by Douady Hubbard, extends previous work second author Mihaljevi\'c more restrictive classes functions.