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OverviewThe 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, Güting, 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. Full Product DetailsAuthor: Fritz Schweiger (Department of Mathematics, Department of Mathematics, University of Salzburg)Publisher: Oxford University Press Imprint: Oxford University Press Dimensions: Width: 16.20cm , Height: 1.80cm , Length: 24.10cm Weight: 0.490kg ISBN: 9780198506867ISBN 10: 0198506864 Pages: 244 Publication Date: 24 August 2000 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of ContentsReviewsIt 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 Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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