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Coarse entropy

Volume 255 / 2021

William Geller, Michał Misiurewicz 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.

Authors

  • William GellerDepartment of Mathematical Sciences
    Indiana University – Purdue University Indianapolis
    402 N. Blackford Street
    Indianapolis, IN 46202, U.S.A.
    e-mail
  • Michał MisiurewiczDepartment of Mathematical Sciences
    Indiana University – Purdue University Indianapolis
    402 N. Blackford Street
    Indianapolis, IN 46202, U.S.A.
    e-mail

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