Schweiger F. Multidimensional continued fractions

Oxford: Oxford University Press, 2000. — 216 p.Piecewise fractional linear maps Brentjes’ formalism
Ergodic theory of fibred systems
Jacobi—Perron algorithm
Basic definitions
Convergence results
Ergodic properties
Giiting’s algorithm
Brun’s algorithm
Subtractive version
Multiplicative acceleration
Selmer’s algorithm
Subtractive version
The division algorithm
Generalized subtractive 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 Poincaré algorithm
Dimension of exceptional setsThe Dirichlet series of a set
A Kuzmin theorem
Some applications