•  
  •  
 
The Mathematics Enthusiast

Authors

Jean Dayantis

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

Included in

Mathematics Commons

Share

COinS