Generalized continued fractions and ergodic theory (Q1125642)

The author constructs a new theory of generalized continued fractions, \((A,\omega)\)-continued fractions, for vectors \(\omega=(\omega_1,\dots,\omega_n)\) with \(0\leq\omega_s<1\) (\(s=1,\dots,n\)) and some map \(A\) of real \(n\)-dimensional space. This theory is applied to solve some problems of analysis and number theory: finding the estimates of Weyl sums and the remainder terms in the laws of distribution and joint distribution of fractional parts of the values of polynomials.