
Multidimensional Continued Fractions
Fritz Schweiger(Author)
Oxford University Press
Published on 24. August 2000
Book
Hardback
244 pages
978-0-19-850686-7 (ISBN)
Description
The book gives an up to date overview of various aspects of multidimensional continued fractions, which are here defined through iteration of piecewise fractional linear maps. This includes the algorithms of Jacobi-Perron, Gueting, Brun, and Selmer but it also includes continued fractions on simplices which are related to interval exchange maps or the Parry-Daniels map. New classes of subtractive algorithms are also included and the metric properties of these algorithms can be therefore investigated by methods of ergodic theory. The recent connection between multiplicative ergodic theory and Diophantine approximation presented, as well as several results on convergence and Perron's approach to periodicity, which has never appeared in book despite being published in 1907. Further chapters include the basic properties of continued fractions in the complex plane, connections with Hausdorff dimension and the Kuzmin theory for multidimensional maps.
Reviews / Votes
It can be warmly recommended to all readers interested in this difficult theory. * EMS * ... will serve as a reference book for anyone interested in this subject in the years to come. * Zentralblatt Mathematik *More details
Language
English
Place of publication
Oxford
United Kingdom
Target group
Professional and scholarly
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 18 mm
Weight
534 gr
ISBN-13
978-0-19-850686-7 (9780198506867)
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Schweitzer Classification