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 in a consistent way.