Wave Functions at the Critical Kolmogorov-Arnol'd-Moser Surface

A quantum system whose classical limit is at the critical threshold to global chaos is studied, i.e., in the small Planck's constant limit the last invariant torus is about to disappear. The quantum states are compared with classical phase-space structure near this torus. We exhibit the extension of the scaling properties of the latter to the quantum regime and find a new scaling of the quantum eigenvalues.