Coarse entropy
Volume 255 / 2021
Fundamenta Mathematicae 255 (2021), 91-109
MSC: 37B40, 51F30.
DOI: 10.4064/fm932-12-2020
Published online: 2 March 2021
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 $(n,\varepsilon )$-separated or $(n,\varepsilon )$-spanning sets. However, we have to let $\varepsilon $ go to infinity rather than to zero.
