International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 4, Pages 251-260

p-adic difference-difference Lotka-Volterra equation and ultra-discrete limit

Shigeki Matsutani

8-21-1 Higashi-Linkan Sagamihara, 228-0811, Japan

Received 28 August 2000; Revised 8 March 2001

Copyright © 2001 Shigeki Matsutani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the difference-difference Lotka-Volterra equations in p-adic number space and its p-adic valuation version. We point out that the structure of the space given by taking the ultra-discrete limit is the same as that of the p-adic valuation space. Since ultra-discrete limit can be regarded as a classical limit of a quantum object, it implies that a correspondence between classical and quantum objects might be associated with valuation theory.