Remarks on the Ergodic Theory of the Continued Fractions

Tibor Šalát

Displaying similar documents to “Remarks on the Ergodic Theory of the Continued Fractions”

Algebraic and ergodic properties of a new continued fraction algorithm with non-decreasing partial quotients

Yusuf Hartono, Cor Kraaikamp, Fritz Schweiger (2002)

Journal de théorie des nombres de Bordeaux

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In this paper the Engel continued fraction (ECF) expansion of any $x \in (0, 1)$ is introduced. Basic and ergodic properties of this expansion are studied. Also the relation between the ECF and F. Ryde’s (MNK) is studied.

'The mother of all continued fractions'

Karma Dajani, Cor Kraaikamp (2000)

Colloquium Mathematicae

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We give the relationship between regular continued fractions and Lehner fractions, using a procedure known as insertion}. Starting from the regular continued fraction expansion of any real irrational x, when the maximal number of insertions is applied one obtains the Lehner fraction of x. Insertions (and singularizations) show how these (and other) continued fraction expansions are related. We also investigate the relation between Lehner fractions and the Farey expansion (also known...

A note on the approximation by continued fractions under an extra condition.

Dajani, Karma, Kraaikamp, Cor (1998)

The New York Journal of Mathematics [electronic only]

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On a theorem of Legendre in the theory of continued fractions

Dominique Barbolosi, Hendrik Jager (1994)

Journal de théorie des nombres de Bordeaux

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A Wirsing-type approach to some continued fraction expansion.

Sebe, Gabriela Ileana (2005)

International Journal of Mathematics and Mathematical Sciences

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Simple Continued Fractions and Their Convergents

Bo Li, Yan Zhang, Artur Korniłowicz (2006)

Formalized Mathematics

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The article introduces simple continued fractions. They are defined as an infinite sequence of integers. The characterization of rational numbers in terms of simple continued fractions is shown. We also give definitions of convergents of continued fractions, and several important properties of simple continued fractions and their convergents.