Ultradiscretization of solvable chaotic maps and the tropical geometry
AbstractWe consider a certain one-dimensional solvable chaotic map arising from the duplication formula of elliptic function, which is a generalization of the logistic map. Applying the ultradiscretization, we obtain the tent map and its general solution simultaneously. We then discuss the tropical geometric interpretation of the tent map; it arises from the duplication map of a certain tropical plane biquadratic curve. If time permits, I will mention on the map arising from the m-th multiplication formula of the elliptic function, and recent result on a certain two-dimensional map.
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