Open Access
2007 On the Singularization of the Two-Dimensional Jacobi--Perron Algorithm
B. Schratzberger
Experiment. Math. 16(4): 441-454 (2007).


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.


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B. Schratzberger. "On the Singularization of the Two-Dimensional Jacobi--Perron Algorithm." Experiment. Math. 16 (4) 441 - 454, 2007.


Published: 2007
First available in Project Euclid: 6 March 2008

zbMATH: 1220.11094
MathSciNet: MR2378485

Primary: 11K50

Keywords: Jacobi--Perron algorithm , Podsypanin algorithm , S-expansions , singularization

Rights: Copyright © 2007 A K Peters, Ltd.

Vol.16 • No. 4 • 2007
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