Multidimensional Continued Fractions

By: Fritz Schweiger

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Hardcover | 1 October 2000

At a Glance

Hardcover
244 Pages

Dimensions(cm)
23.39 x 15.6 x 1.42

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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, 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.

Industry Reviews

"It is thanks to F. Schweiger that the extensive literature on multidimensional continued fractions, especially those which can be described by fractional linear maps can now be seen from a more systematic point of view and it is thanks to the publishing company for having won a real expert for this
project. . .The book is very carefully written and indispensable for all experts working in this field."--
onatshefte Fuer Mathematik

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Number Theory Applied Mathematics Chaos Theory Optimisation Linear Programming Combinatorics & Graph Theory Science Physics Probability & Statistics

Piecewise fractional linear maps
Brentjes' formalism
Ergodic theory of fibred systems
Jacobi-Perron algorithm
Basic definitions
Convergence results
Ergodic properties
Guting's algorithm
Subtractive version
Multiplicative acceleration
Selmer's algorithm
Subtractive version
The division algorithm
Generalized substractive algorithms
Fully subtractive algorithms
Skew products
Continued fractions on simplices
Fractional linear maps
Interval exchange transformations
The convergence method of Greiter
Periodic expansions
Convergence and rational dependence
Diophantine approximation
Exponents of approximation
Perron's identity
Results on convergence
The second Lyapunov exponent
Periodic Jacobi-Perron algorithms
Convergence for periodic expansions
Volume as a measure of approximation
Complex continued fractions
The Poincare alogrithm
Dimension of exceptional sets
Introduction
The Dirichlet series of a set
A Kuzmin theorem
Some applications
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Multidimensional Continued Fractions

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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