Abstract
We prove the existence (as h→0) of the singular continuous («Cantor-like») spectrum for the Fermi-Ulam model on a torus for a certain phase-space domain and an irrational (diophantine) ratio of the minimum distance between the walls to the oscillation amplitude of the moving wall. Varied scenario of the stabilizing and destabilizing spectral transitions are observed in the limit of vanishing Planck's constant, and their relation with the qualitative changes in the quasienergy eigenstates is brought out
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