Bohr-Sommerfeld Quantization of Periodic Orbits

We show, that the canonical invariant part of $\mathrm{\hslash }$ corrections to the Gutzwiller trace formula and the Gutzwiller-Voros spectral determinant can be computed by the Bohr-Sommerfeld quantization rules, which usually apply for integrable systems. We argue that the information content of the classical action and stability can be used more effectively than in the usual treatment. We demonstrate the improvement of precision on the example of the three disk scattering system.