On the Singularization of the Two-Dimensional Jacobi--Perron Algorithm

Schratzberger, B.

Experiment. Math., Tome 16 (2007) no. 1, p. 441-454 / Harvested from Project Euclid

Résumé

We present a constructive method to convert the (two-dimensional) Jacobi--Perron evolution of $(x_1,x_2) \in [0,1]^2$ into the corresponding evolution of Podsypanin, and vice versa. A similar approach allows us to extend the result to Brun's algorithm. The method, based on the techniques of singularization and insertion, is built up in steps. From experiments, we assume that each step terminates after finitely many states almost everywhere.

Publié le : 2007-05-15
Classification: Jacobi--Perron algorithm, Podsypanin algorithm, singularization, S-expansions, 11K50

@article{1204836514,
     author = {Schratzberger, B.},
     title = {On the Singularization of the Two-Dimensional Jacobi--Perron Algorithm},
     journal = {Experiment. Math.},
     volume = {16},
     number = {1},
     year = {2007},
     pages = { 441-454},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1204836514}
}

Schratzberger, B. On the Singularization of the Two-Dimensional Jacobi--Perron Algorithm. Experiment. Math., Tome 16 (2007) no. 1, pp.  441-454. http://gdmltest.u-ga.fr/item/1204836514/