Volume
7
Issue
2-3
Abstract
After briefly recalling the concepts of recurrence and chaos in physics, the recurrence properties of arithmetic sets are examined following Gauss’ method, as exposed in part three of his Disquisitiones Arithmeticae. This problem in number theory is related to the physical problem of recurrence in deterministic chaos. Most possible forms of moduli are examined in detail with respect to their recurrence properties, for application to the generalized Bernoulli mapping. The emphasis is put on period lengths, rather than on congruences. In an annex the recurrence properties of Arnold’s cat map are briefly examined.
First Page
223
Last Page
246
Recommended Citation
Dayantis, Jean
(2010)
"Chaos in Physics and recurrence in Arithmetic Sets,"
The Mathematics Enthusiast: Vol. 7
:
No.
2
, Article 4.
DOI: https://doi.org/10.54870/1551-3440.1185
Available at:
https://scholarworks.umt.edu/tme/vol7/iss2/4
Digital Object Identifier (DOI)
10.54870/1551-3440.1185
