The aim of this paper is to review the classical limit of Quantum Mechanics
and to precise the well known threat of chaos (and fundamental graininess)to
the correspondence principle. We will introduce a formalism for this classical
limit that allows us to find the surfaces defined by the constants of the
motion in phase space. Then in the integrable case we will find the classical
trajectories, and in the non-integrable one the fact that regular initial cells
become "amoeboid-like". This deformations and their consequences can be
considered as a threat to the correspondence principle unless we take into
account the characteristic timescales of quantum chaos. Essentially we present
an analysis of the problem similar to the one of Omn\`{e}s [10,11], but with a
simpler mathematical structure.Comment: 27 pages, 6 figure
