A simple proof of the exponential convergence of the modified Jacobi-Perron algorithm

Ergodic Theory and Dynamical Systems

Volumn 19, Issue 4, 1999, Pages 1077-1083

  Meester, Ronald ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033472288     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385799133960     Document Type: Article

References (12)

1. Bernstein, L. The Jacobi-Perron Algorithm. Its Theory and Application (Springer Lecture Notes, 207). Springer, New York, 1971.
2. Brentjes, A. J. Multi-dimensional Continued Fraction Algorithms. Math. Centre, Amsterdam, 1981.
3. Fujita, T., Ito, S., Keane, M. and Ohtsuki, M. On almost everywhere exponential convergence of the modified Jacobi-Perron algorithm: a corrected proof. Ergod. Th. & Dynam. Sys. 16(6) (1996), 1345-1352.
4. Ito, S., Keane, M. S. and Ohtsuki, M. Almost everywhere exponential convergence of the modified Jacobi-Perron algorithm. Ergod. Th. & Dynam. Sys. 13 (1993), 319-334.
5. Kraaikamp, C. and Meester, R. Convergence of continued fraction type algorithms and generators. Monatshefte für Mathematik 125 (1998), 1-14.
6. Paley, R. E. A. C. and Ursell, U. B. Continued fractions in several dimensions. Proc. Camb. Phil. Soc. 26 (1930), 127-144.
7. Podsypanin, E. V. A generalization of the algorithm for continued fractions related to the algorithm of Viggo Brunn. Studies in Number Theory (LOMI), 4. Zap. Naucn. Sem. Leningrad Otdel. Mat. Inst. Steklov 67 (1977), 184-194. (English translation: J. Sov. Math. 16 (1981), 885-893.)
8. Podsypanin, E. V. A generalization of the algorithm for continued fractions related to the algorithm of Viggo Brunn. Studies in Number Theory (LOMI), 4. Zap. Naucn. Sem. Leningrad Otdel. Mat. Inst. Steklov 67 (1977), 184-194. (English translation: J. Sov. Math. 16 (1981), 885-893.)
9. Schweiger, F. The Metrical Theory of the Jacobi-Perron Algorithm (Springer Lecture Notes, 334). Springer, New York, 1973.
10. Schweiger, F. A Modified Jacobi-Perron Algorithm with Explicitly Given Invariant Measure (Springer Lecture Notes, 729). Springer, New York, 1978.
11. Schweiger, F. Invariant measures for maps of continued fraction type. J. Number Theory 39 (1991), 162-174.
12. Schweiger, F. The exponent of convergence for the 2-dimensional Jacobi-Perron algorithm. Proc. Conf. on Analytic and Elementary Number Theory. Eds W. G. Nowak and J. Schoissengeier. Vienna, 1996, pp 207-213.