  In this paper we study the dynamics and ergodic theory of certain economic
models which are implicitly defined. We consider 1-dimensional and
2-dimensional overlapping generations models, a cash-in-advance model,
heterogeneous markets and a cobweb model with adaptive adjustment. We consider
the inverse limit spaces of certain chaotic invariant fractal sets and their
metric, ergodic and stability properties. The inverse limits give the set of
intertemporal perfect foresight equilibria for the economic problem considered.
First we show that the inverse limits of these models are stable under
perturbations. We prove that the inverse limits are expansive and have
specification property. We then employ utility functions on inverse limits in
our case. We give two ways to rank such utility functions. First, when
perturbing certain dynamical systems, we rank utility functions in terms of
their \textit{average values} with respect to invariant probability measures on
inverse limits, especially with respect to measures of maximal entropy. For
families of certain unimodal maps we can adjust both the discount factor and
the system parameters in order to obtain maximal average value of the utility.
The second way to rank utility functions (for more general maps on hyperbolic
sets) will be to use equilibrium measures of these utility functions on inverse
limits; they optimize average values of utility functions while \textit{at the
same time} keeping the disorder in the system as low as possible in the long
run.
