### Hyperbolic Properties of Coupled Expanding Maps

Jose Koiller

Abstract.
We study the hyperbolic properties of a class of coupled expanding
circle maps. These maps are defined by composing the product of an
arbitrary number d of circle maps (the "local systems") with a certain
"coupling" or "averaging" map on the d-torus. The coupling map is
specified via a weighted graph whose vertices represent the local
systems and whose edges represent the interaction strength between
them. We show how hyperbolic behavior (uniform or partial, depending
on coupling strengths) naturally arises in this setting.