论文标题
粗熵
Coarse entropy
论文作者
论文摘要
粗几何研究大规模的度量空间。我们的目标是从粗略的角度研究动态。为此，我们引入了拓扑熵的粗糙版本，适用于无限制的度量空间，与此类空间的粗略视角一致。与通常的拓扑熵一样，粗熵测量轨道的差异。遵循鲍恩的想法，我们使用$（n，\ varepsilon）$ - 分离或$（n，\ varepsilon）$跨度集。但是，我们必须让$ \ varepsilon $转到无穷大，而不是零。
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.
