ABSTRACT
The chapter introduces another type of continued fraction as a modification of the already known one due to Hirzebruch and Jung. After studing the convergence of this new expansion, it is proved that the mapping Ha generating the generalized Hirzebruch-Jung continued fractions is measure-preserving and ergodic respect to a Borel measure ϑa on [0, 1], which in turn is applied to obtain extensions of Khintchine and Levy formulas. The chapter concludes by defining a Khintchine type constant Ka∗ and obtaining a formula that links it with the one studied in Chapter 5.
