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

Matsutani, Shigeki

doi:https://doi.org/10.1155/S0161171201010808

International Journal of Mathematics and Mathematical Sciences

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Volume 27 |Article ID 549451 | https://doi.org/10.1155/S0161171201010808

Shigeki Matsutani, "p-adic difference-difference Lotka-Volterra equation and ultra-discrete limit", International Journal of Mathematics and Mathematical Sciences, vol. 27, Article ID 549451, 10 pages, 2001. https://doi.org/10.1155/S0161171201010808

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

Shigeki Matsutani¹

¹8-21-1 Higashi-Linkan Sagamihara, 228-0811, Japan

Received28 Aug 2000

Revised08 Mar 2001

Abstract

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.

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Copyright © 2001 Hindawi Publishing Corporation. 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.

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