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

Doug Hensley

doi:10.3934/dcds.2012.32.2417

Article Contents

2012, Volume 32, Issue 7: 2417-2436. Doi: 10.3934/dcds.2012.32.2417

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

Doug Hensley^1,

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

Received: November 30, 2009

Revised: July 31, 2011

Published: June 2012

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Abstract

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.

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

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References

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