Metrical and Ergodic Theory of Continued Fraction Algorithms
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Beschreibung
This monograph presents the work of the authors in metrical theory of continued fractions in the last two decades. The monograph cuts a particular path through this extensive theory and describes the theory in its current form for three families of continued fractions, namely, θ-continued fractions, N-continued fractions, and generalized Rényi continued fractions. The book systematically lays out the required preliminaries, making the book easy to read. This monograph provides a solid introduction into the theory of continued fractions.
The book is intended for researchers in metrical theory, as well as advanced graduate students and mathematicians interested in this field.
This monograph presents the work of the authors in metrical theory of continued fractions in the last two decades. The monograph cuts a particular path through this extensive theory and describes the theory in its current form for three families of continued fractions, namely, θ-continued fractions, N-continued fractions, and generalized Rényi continued fractions. The book systematically lays out the required preliminaries, making the book easy to read. This monograph provides a solid introduction into the theory of continued fractions.
The book is intended for researchers in metrical theory, as well as advanced graduate students and mathematicians interested in this field.
Studies various algorithms for the representation of real numbers via sequences of integers Presents the authors most important original results in the metrical theory of continued fractions Develops classical results on the speed of convergence by Gauss algorithm and applies these to different generalisations
Autor*in
Gabriela Ileana Sebe
Themen in »Metrical and Ergodic Theory of Continued Fraction Algorithms«
Metrical Theory Ergodic Theory Continued Fractions Markov Chains Probability Measure
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“The authors wrote many papers on the metric theory of continued fractions in the last twenty years. This monograph is a synthesis of their work. ... The book is well-written, it is reasonably easy to read. Furthermore it contains a useful list of 76 references. All this makes this book a must-read for mathematicians working in (or curious about) this field.” (Jean-Paul Allouche, zbMATH 1578.11006, 2026)
“The authors have made many contributions to the metric theory of continued fractions over the last twenty years, and this is a coherent account of some of this work. … The book is a carefully written account of these three families and contains an extensive bibliography of these themes. It will be of interest to researchers studying any kind of continued fraction expansions from both the ergodic theory and the number theory point of view.” (Thomas Ward, Mathematical Reviews, May, 2026)
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