The quantum chaos conjecture and generalized continued fractions

The proof of the quantum chaos conjecture is given for a class of systems including as a special case the model of a rotating particle under the action of periodic impulse perturbations. (The distribution of the distances between adjacent energy levels is close to the Poisson distribution and differs from it by terms of the third order of smallness.) The proof reduces to a result in number theory on the distribution of the distances between adjacent fractional parts of values of a polynomial, while the estimate of the remainder term is based on the new theory of generalized continued fractions for vectors.