Continued fractions, Cantor sets, Hausdorff dimension, and transfer operators and their analytic extension

We survey the dynamical systems side of the theory of continued fractions and touch on some of the frontiers of the subject. Ergodic theory plays a role. The work of Baladi and Vallee is discussed. Power series methods that allow for the computation of various numbers such as the Hausdorff dimension of a continued fraction Cantor set, or the Wirsing constant of a particular continued fraction algorithm, to high accuracy, are also discussed.