On a new continued fraction expansion with non-decreasing partial quotients (Q706214)

Recently, \textit{Y. Hartono}, \textit{C. Kraaikamp} and \textit{F. Schweiger} [in: ``Algebraic and ergodic properties of a new continued fraction algorithm with non-decreasing partial quotients'', J. Théor. Nombres Bordx. 14, No. 2, 497--516 (2002; Zbl 1067.11042)] have introduced a new continued fraction algorithm with non-decreasing partial quotients, called the Engel continued fraction (ECF) expansion. In Section 2 the ergodic properties of the operator \(T_E\) associated with ECF are studied. It is showed that \(T_E\) has no finite invariant measure equivalent to the Lebesgue measure \(\lambda\), but that \(T_E\) has infinitely many \(\sigma\)-finite, infinite invariant measures. Section 3 is devoted to the study of the metric properties of the digits. Also, some fractal properties of exceptional sets are mentioned.