Arithmetic and ergodic properties of 'flipped' continued fraction algorithms
K. Dajani, C. Kraaikamp, V. Masarotto (2012)
Acta Arithmetica
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K. Dajani, C. Kraaikamp, V. Masarotto (2012)
Acta Arithmetica
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Asmus L. Schmidt (1982)
Monatshefte für Mathematik
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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...
C. Ryll-Nardzewski (1951)
Studia Mathematica
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Dajani, Karma, Kraaikamp, Cor (1998)
The New York Journal of Mathematics [electronic only]
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Hitoshi Nakada (1988)
Monatshefte für Mathematik
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Kentaro Nakaishi (2006)
Acta Arithmetica
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M.S. Waterman, W.A. Beyer (1972)
Numerische Mathematik
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Donald S. Ornstein (1975)
Publications mathématiques et informatique de Rennes
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Zbigniew S. Kowalski (1984)
Colloquium Mathematicae
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A. Al-Hussaini (1974)
Annales Polonici Mathematici
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Nishishiraho, Toshihiko (1998)
Journal of Convex Analysis
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Roland Zweimüller (2004)
Colloquium Mathematicae
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We present a very quick and easy proof of the classical Stepanov-Hopf ratio ergodic theorem, deriving it from Birkhoff's ergodic theorem by a simple inducing argument.
Janusz Woś (1987)
Colloquium Mathematicae
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