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A new class of continued fraction expansions. (English) Zbl 0721.11029
A new approach to the metrical theory of several semi-regular continued fractions is given: the so-called singularization process (which essentially can be found in O. Perron’s classic book “Die Lehre von den Kettenbr├╝chen” (1929; JFM 55.0262.09)) is related to the first return map on certain subsets of the unit square (the complements of the so- called “singularization areas”). In this way a surprisingly insightful explanation of the statistical properties of the nearest integer continued fraction, Hurwitz’ singular continued fraction, Minkowski’s diagonal expansion and Wieb Bosma’s optimal continued fraction are obtained.

11K50 Metric theory of continued fractions
11A55 Continued fractions
11J70 Continued fractions and generalizations
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