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

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  • 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 Vallée 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.
    Mathematics Subject Classification: Primary: 11A55, 11K50, 11K55, 11J70; Secondary: 11K60, 11Y60, 11Y65, 30B10.

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    P. Flajolet and B. Vallée, On the Gauss-Kuzmin-Wirsing constant, unpublished note, 1995.

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    E. WirsingOn the theorem of Gauss-Kusmin-Lévy and a Frobenius-type theorem for function spaces, V. Acta Arith., 24 (1973/74), 507-528.

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