Coupled map graphs
Jose Koiller

We introduce a class of dynamical systems obtained by coupling a
finite number of expanding cicle maps (the "local systems"). The
admitted coupling configurations are quite arbitrary, and most
conveniently described via "coupling graphs" whose vertices represent
the local systems. We show how hyperbolic behavior (uniform or
partial, depending on coupling strenghts) naturally arises in this
setting, and we construct natural invariant measures in some cases.