Articles liés à Multidimensional Continued Fractions

Multidimensional Continued Fractions - Couverture rigide

Schweiger, Fritz

 
9780198506867: Multidimensional Continued Fractions
Couverture rigide
ISBN 10 : 0198506864 ISBN 13 : 9780198506867
Editeur : Oxford University Press, 2000

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

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.

Revue de presse

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)

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Oxford University Press
Date d'édition
2000
Langue
anglais
ISBN 10 
0198506864
ISBN 13 
9780198506867
Reliure
Relié
Nombre de pages
244
Coordonnées du fabricant
non disponible
Personne responsable
Ufficio Anagrafiche Messaggerie
ufficio.anagrafiche@meli.it

Via Verdi, 8
Assago Milano
20090
Italie