We define iterated monodromy groups of more general structures than partial
self-covering. This generalization makes it possible to define a natural notion
of a combinatorial model of an expanding dynamical system. We prove that a
naturally defined "Julia set" of the generalized dynamical systems depends only
on the associated iterated monodromy group. We show then that the Julia set of
every expanding dynamical system is an inverse limit of simplicial complexes
constructed by inductive cut-and-paste rules.Comment: The new version differs substantially from the first one. Many parts
are moved to other (mostly future) papers, the main open question of the
first version is solve