  This paper is part 1 of a series of papers culminating in the result that
measure preserving diffeomorphisms of the disc or 2-torus are unclassifiable.
It also addresses another classical problem: which abstract measure preserving
systems are realizable as smooth diffeomorphisms of a compact manifold? The
main result of this paper gives new symbolic representations of the
Anosov-Katok diffeomorphisms.
