×

zbMATH — the first resource for mathematics

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.

MSC:
11K50 Metric theory of continued fractions
11A55 Continued fractions
11J70 Continued fractions and generalizations
PDF BibTeX XML Cite
Full Text: DOI EuDML