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