Articoli correlati a Multidimensional Continued Fractions
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.
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Recensione:
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)
... will serve as a reference book for anyone interested in this subject in the years to come. (Zentralblatt Mathematik)
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- EditoreOUP Oxford
- Data di pubblicazione2000
- ISBN 10 0198506864
- ISBN 13 9780198506867
- RilegaturaCopertina rigida
- Numero di pagine244
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Multidimensional Continued Fractions (Hardcover)
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Descrizione libro Hardcover. Condizione: new. Hardcover. 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 thesealgorithms 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 onconvergence 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. Multidimensional continued fractions form an area of research within number theory. Recently the topic has been linked to research in dynamical systems, and mathematical physics, which means that some of the results discovered in this area have applications in describing physical systems. This book gives a comprehensive and up to date overview of recent research in the area. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Codice articolo 9780198506867
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Multidimensional Continued Fractions [Hardcover] Schweiger, Fritz (eng)
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ISBN 10: 0198506864
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Descrizione libro Hardcover. Condizione: new. Hardcover. 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 thesealgorithms 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 onconvergence 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. Multidimensional continued fractions form an area of research within number theory. Recently the topic has been linked to research in dynamical systems, and mathematical physics, which means that some of the results discovered in this area have applications in describing physical systems. This book gives a comprehensive and up to date overview of recent research in the area. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9780198506867
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Multidimensional Continued Fractions
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Descrizione libro Buch. Condizione: Neu. Neuware - Multidimensional continued fractions form an area of research within number theory. Recently the topic has been linked to research in dynamical systems, and mathematical physics, which means that some of the results discovered in this area have applications in describing physical systems. This book gives a comprehensive and up to date overview of recent research in the area. Codice articolo 9780198506867
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