Multidimensional Continued Fractions

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Fritz Schweiger (Department of Mathematics, Department of Mathematics, University of Salzburg)

Multidimensional Continued Fractions

Fritz Schweiger (Department of Mathematics, Department of Mathematics, University of Salzburg)

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English

Oxford University Press
01 October 2000

Number theory; Calculus & mathematical analysis; Linear programming; Combinatorics & graph theory

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, 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.

By: Fritz Schweiger (Department of Mathematics Department of Mathematics University of Salzburg)
Imprint: Oxford University Press
Country of Publication: United Kingdom
Dimensions: Height: 241mm, Width: 162mm, Spine: 18mm
Weight: 490g
ISBN: 9780198506867
ISBN 10: 0198506864
Pages: 244
Publication Date: 01 October 2000
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Reviews for Multidimensional Continued Fractions

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