# American Institute of Mathematical Sciences

July  2012, 32(7): 2417-2436. doi: 10.3934/dcds.2012.32.2417

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

 1 Mathematics Department, Texas A&M University, College Station, TX 77843-3368, United States

Received  December 2009 Revised  August 2011 Published  March 2012

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.
Citation: Doug Hensley. Continued fractions, Cantor sets, Hausdorff dimension, and transfer operators and their analytic extension. Discrete & Continuous Dynamical Systems - A, 2012, 32 (7) : 2417-2436. doi: 10.3934/dcds.2012.32.2417
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