On polyharmonic operators with limit-periodic potential in dimension two

This is an announcement of the following results. We consider a polyharmonic operator H = (-Delta)(l) + V (x) in dimension two with l >= 6 and V (x) being a limit-periodic potential. We prove that the spectrum of H contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves at the high-energy region. Second, the isoenergetic curves in the space of momenta corresponding to these eigenfunctions have the form of slightly distorted circles with holes (Cantor-type structure). Third, the spectrum corresponding to the eigenfunctions (the semiaxis) is absolutely continuous.