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, * -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

Autorentext

Dan Lascu i s a professor of mathematics at the Romanian Naval Academy.

Gabriela Ileana Sebe is a professor of mathematics at the National University of Science and Technology Politehnica and scientific researcher at "Gheorghe Mihoc-Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics( ISMMA) of the Romanian Academy.

Inhalt

• 1. Introduction.- 2. * -Continued Fraction Expansions.- 3. N* -Continued Fractions.- 4. Generalized Rényi Continued Fractions.- 5. Comparing the Efficiency of Different Continued Fraction Algorithms.