| 概要 | We develop a new mathematical model for describing a dynamical system at limited resolution (or finite scale), and we give precise meaning to the notion of a dynamical system having some property at finite resolution. Open covers are used to approximate the topology of the phase space in a finite way, and the dynamical system is represented by means of a combinatorial multivalued map. We translate notions of transitivity and mixing known for general dynamical systems into the finite setting. Moreover, we formulate equivalent conditions for these properties in terms of graphs, and provide effective algorithms for their verification. As an application we show that the H\'enon attractor is topologically mixing at all resolutions coarser than $10^{-5}$. This is joint work with Stefano Luzzatto. |