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

international journal of mathematics and mathematical sciences

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$p$" id="E1"><mml:mi>p</mml:mi></mml:math>-adic difference-difference Lotka-Volterra equation and ultra-discrete limit

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