Coarse entropy
William Geller and Michał Misiurewicz
Abstract
Coarse geometry studies metric spaces on the large scale. Our goal
here is to study dynamics from a coarse point of view. To this end we
introduce a coarse version of topological entropy, suitable for
unbounded metric spaces, consistent with the coarse perspective on
such spaces. As is the case with the usual topological entropy, the
coarse entropy measures the divergence of orbits. Following Bowen's
ideas, we use (n,ε)-separated or
(n,ε)-spanning sets. However, we have to let
 ε  go to infinity rather than to zero.