A proof that the three-dimensional Gauss algorithm is strongly convergent almost everywhere is given. This algorithm is equivalent to Brun's algorithm and to the modified Jacobi-Perron algorithm considered by Podsypanin and Schweiger. The proof involves the rigorous computer assisted estimation of the largest Lyapunov exponent of a cocycle associated to the algorithm. To the best of my knowledge, this is the first proof of almost everywhere strong convergence of a Jacobi-Perron type algorithm in dimension greater than two.
|Number of pages||11|
|Publication status||Published - 2002|
- Brun's algorithm
- Jacobi-Perron algorithm
- Lyapunov exponents
- Multidimensional continued fractions
- Strong convergence