Some Borel measures associated with the generalized Collatz mapping
Matthews, K.
Colloquium Mathematicae, Tome 63 (1992), p. 191-202 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

This paper is a continuation of a recent paper [2], in which the authors studied some Markov matrices arising from a mapping T:ℤ → ℤ, which generalizes the famous 3x+1 mapping of Collatz. We extended T to a mapping of the polyadic numbers ℤ^ and construct finitely many ergodic Borel measures on ℤ^ which heuristically explain the limiting frequencies in congruence classes, observed for integer trajectories.

Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:210145 
@article{bwmeta1.element.bwnjournal-article-cmv63i2p191bwm,
     author = {K. Matthews},
     title = {Some Borel measures associated with the generalized Collatz mapping},
     journal = {Colloquium Mathematicae},
     volume = {63},
     year = {1992},
     pages = {191-202},
     zbl = {0769.11006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv63i2p191bwm}
}

Matthews, K. Some Borel measures associated with the generalized Collatz mapping. Colloquium Mathematicae, Tome 63 (1992) pp. 191-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv63i2p191bwm/

[000] [1] P. Billingsley, Ergodic Theory and Information, Wiley, New York 1965. | Zbl 0141.16702

[001] [2] R. N. Buttsworth and K. R. Matthews, On some Markov matrices arising from the generalized Collatz mapping, Acta Arith. 55 (1990), 43-57. | Zbl 0653.10004

[002] [3] K. L. Chung, Markov Chains, Springer, Berlin 1960. | Zbl 0122.36601

[003] [4] K. R. Matthews and A. M. Watts, A generalization of Hasse's generalization of the Syracuse algorithm, Acta Arith. 43 (1984), 167-175. | Zbl 0479.10006

[004] [5] K. R. Matthews and A. M. Watts, A Markov approach to the generalized Syracuse algorithm, ibid. 45 (1985), 29-42. | Zbl 0521.10008

[005] [6] K. R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York 1967. | Zbl 0153.19101

[006] [7] M. Pearl, Matrix Theory and Finite Mathematics, McGraw-Hill, New York 1973.

[007] [8] A. G. Postnikov, Introduction to Analytic Number Theory, Amer. Math. Soc., Providence, R.I., 1988. | Zbl 0641.10001

[008] [9] A. Rényi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hungar. 8 (1957), 477-493. | Zbl 0079.08901