  A generalization of the Weyl law to systems with a sharply divided mixed
phase space is proposed. The ansatz is composed of the usual Weyl term which
counts the number of states in regular islands and a term associated with
sticky regions in phase space. For a piecewise linear map, we numerically check
the validity of our hypothesis, and find good agreement not only for the case
with a sharply divided phase space, but also for the case where tiny island
chains surround the main regular island. For the latter case, a non-trivial
power law exponent appears in the survival probability of classical escaping
orbits, which may provide a clue to develop the Weyl law for more generic mixed
systems.
