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Equipartition of interval partitions and an application to number theory
Author(s):
Karma
Dajani;
Adam
Fieldsteel
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3453-3460.
MSC (1991):
Primary 11Kxx, 28Dxx
Posted:
June 27, 2001
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Abstract:
We give wider application and simpler proofs of results describing the rate at which the digits of one number-theoretic expansion determine those of another. The proofs are based on general measure-theoretic covering arguments and not on the dynamics of specific maps.
References:
- [BBDK]
- Barrionuevo, J., R.M. Burton, K. Dajani and C. Kraaikamp - Ergodic properties of generalized Lúroth series, Acta Arithm., 74 (1996), 311-327. MR 97b:11104
- [BDK]
- Bosma, W., K. Dajani and C. Kraaikamp - Entropy and counting correct digits, University of Nijmegen, report no. 9925, 1999. http://www-math.sci.kun.nl /math/onderzoek/reports/reports1999.html
- [B]
- Billingsley, P. - Ergodic Theory and Information, John Wiley and Sons, Inc.; New York-London-Sydney (1965). MR 33:254
- [L]
- Lochs, G. - Vergleich der Genauigkeit von Dezimalbruch und Kettenbruch, Abh. Math. Sem. Hamburg, 27 (1964), 142-144. MR 29:57
- [R]
- Rényi, A. - Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hung. 8 (1957), 472-493. MR 20:3843
- [S]
- Schweiger, F. - Ergodic Theory of Fibred Systems and Metric Number Theory, Oxford University Press, Oxford, 1995. MR 97h:11083
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Additional Information:
Karma
Dajani
Affiliation:
Department of Mathematics, Utrecht University, 3508TA Utrecht, The Netherlands
Email:
dajani@math.uu.nl
Adam
Fieldsteel
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
Email:
afieldsteel@wesleyan.edu
DOI:
10.1090/S0002-9939-01-06299-2
PII:
S 0002-9939(01)06299-2
Keywords:
Entropy,
ergodic,
continued fraction,
number-theoretic fibered map
Received by editor(s):
March 8, 2000
Posted:
June 27, 2001
Additional Notes:
The first author was partially supported by NWO grant no. 61-449
We wish to thank Ethan Coven for useful observations.
Communicated by:
Michael Handel
Copyright of article:
Copyright
2001,
American Mathematical Society
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