THE DISTAL AND ASYMPTOTIC SETS FOR CONTINUED FRACTIONS
Keyword(s):
For continued fraction dynamical system [Formula: see text], we give a classification of the underlying space [Formula: see text] according to the orbit of a given point [Formula: see text]. The sizes of all classes are determined from the viewpoints of measure, Hausdorff dimension and topology. For instance, the Hausdorff dimension of the distal set of [Formula: see text] is one and the Hausdorff dimension of the asymptotic set is either zero or [Formula: see text] according to [Formula: see text] is rational or not.
2018 ◽
Vol 39
(11)
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pp. 3031-3065
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2020 ◽
Vol 16
(07)
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pp. 1433-1447
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2014 ◽
Vol 10
(04)
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pp. 849-857
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2009 ◽
Vol 29
(1)
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pp. 73-109
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2008 ◽
Vol 145
(1)
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pp. 215-225
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