  We prove a general estimate for the Weyl remainder of an elliptic,
semiclassical pseudodifferential operator in terms of volumes of recurrence
sets for the Hamilton flow of its principal symbol. This quantifies earlier
results of Volovoy. Our result particularly improves Weyl remainder exponents
for compact Lie groups and surfaces of revolution. And gives a quantitative
estimate for B\'erard's Weyl remainder in terms of the maximal expansion rate
and topological entropy of the geodesic flow.
