  The classical limit of non-integrable quantum systems is studied. We define
non-integrable quantum systems as those which have, as their classical limit, a
non-integrable classical system. In order to obtain this limit, the
self-induced decoherence approach and the corresponding classical limit are
generalized from integrable to non-integrable systems. In this approach, the
lost of information, usually conceived as the result of a coarse-graining or
the trace of an environment, is produced by a particular choice of the algebra
of observables and the systematic use of mean values, that project the unitary
evolution onto an effective non-unitary one. The decoherence times computed
with this approach coincide with those of the literature. By means of our
method, we can obtain the classical limit of the quantum state of a
non-integrable system, which turns out to be a set of unstable, potentially
chaotic classical trajectories contained in the Wigner transformation of the
quantum state.
