Multidimensional Continued Fractions 9780198506867, 0198506864
303 36 14MB
English Pages [216] Year 2000
Table of contents :
Preface
Contents
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. Güting's algorithm
6. Brun'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 subtractive 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
20. Complex continued fractions
21. The Poincaré algorithm
22. Dimension of exceptional sets
22.1 Introduction
22.2 The Dirichlet series of a set
23. A Kuzmin theorem
24. Some applications
References
A, B
C, D, E, F, G
H, I, J
K, L, M
N, P
R, S
T, V
W, Y, Z
Index
Preface
Contents
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. Güting's algorithm
6. Brun'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 subtractive 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
20. Complex continued fractions
21. The Poincaré algorithm
22. Dimension of exceptional sets
22.1 Introduction
22.2 The Dirichlet series of a set
23. A Kuzmin theorem
24. Some applications
References
A, B
C, D, E, F, G
H, I, J
K, L, M
N, P
R, S
T, V
W, Y, Z
Index
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