  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 all resolutions coarser than a
given number. 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 formulate notions of transitivity and mixing
in the finite resolution setting in a computable and consistent way. 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 Henon attractor is mixing at all resolutions coarser than 10^-5.
