Multidimensional Continued Fractions [Hardcover]

1. Piecewise fractional linear maps
2. Brentjes' formalism
3. Ergodic theory of fibred systems
4. Jacobi-Perron algorithm
4.1. Basic definitions
4.2. Convergence results
4.3. Ergodic properties
5. G??ting's algorithm
6.1. Subtractive version
6.2. Multiplicative acceleration
7. Selmer's algorithm
7.1. Subtractive version
7.2. The division algorithm
8. Generalized substractive algorithms
9. Fully subtractive algorithms
10. Skew products
11. Continued fractions on simplices
11.1. Fractional linear maps
11.2. Interval exchange transformations
12. The convergence method of Greiter
13. Periodic expansions
14. Convergence and rational dependence
15. Diophantine approximation
15.1. Exponents of approximation
15.2. Perron's identity
15.3. Results on convergence
16. The second Lyapunov exponent
17. Periodic Jacobi-Perron algorithms
18. Convergence for periodic expansions
19. Volume as a measure of approximation
20. Complex continued fractions
21. The Poincar?? alogrithm
22. Dimension of exceptional sets
22.1. Introduction
22.2. The Dirichlet series of a set
23. A Kuzmin theorem
24. Some applications
References
Index

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