Multidimensional Continued Fractions
«It can be warmly recommended to all readers interested in this difficult theory.»
EMS
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 on simplices which are related to interval exchange maps or the Parry-Daniels map. Les mer
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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.
Detaljer
- Forlag
- Oxford University Press
- Innbinding
- Innbundet
- Språk
- Engelsk
- ISBN
- 9780198506867
- Utgivelsesår
- 2000
- Format
- 24 x 16 cm
Anmeldelser
«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