Multidimensional Continued Fractions

Hardcover | August 15, 2000

byFritz Schweiger

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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, Guting, Brun, and Selmer but it also includes continued fractions onsimplices 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 ergodictheory 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, connectionswith Hausdorff dimension and the Kuzmin theory for multidimensional maps.

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From the Publisher

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, Guting, Brun, and Selmer but it also includes continued fractions onsimplices which are related to interval excha...

Fritz Schweiger is in the Department of Mathematics at University of Salzburg.
Format:HardcoverDimensions:242 pages, 9.21 × 6.14 × 0.71 inPublished:August 15, 2000Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198506864

ISBN - 13:9780198506867

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