About Imperfect Mushroom Billiards

Imperfections of Bunimovich mushroom Billiards are analyzed. Any experiment will be affected by such imperfections, and it will be necessary to estimate their influence. In particular some of the corners will be rounded and small deviations of the angle of the underside of the mushroom head will be considered. The analysis displayed some unexpected non-generic features. The latter leads to a transition from a perfect mushroom behavior to either an ordinary KAM scenario or an abrupt transition to complete chaos, depending on the sign of the perturbation. The former produces a fractal area of islands and chaos, in fact a KAM scenario, not associated to the large island of stability of the mushroom billiard.