-adic difference-difference Lotka-Volterra equation and ultra-discrete limit
We study the difference-difference Lotka-Volterra equations in -adic number space and its -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 -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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