Weyl laws for open quantum maps

We find Weyl upper bounds for the quantum open baker’s map in semiclassical limit. For number of eigenvalues an annulus, we derive asymptotic bound $\mathcal O(N^\delta)$, where $\delta$ is dimension trapped set and $(2 \pi N)^{-1}$ parameter, which improves upon previous result O(N^{\delta + \epsilon})$. Furthermore, a with explicit dependence on inner radius annulus maps Gevrey cutoffs.