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arXiv · 0803.4062

Ultradiscretization of solvable one-dimensional chaotic maps

Kenji Kajiwara·Atsushi Nobe·Teruhisa Tsuda
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Abstract

We consider the ultradiscretization of a solvable one-dimensional chaotic map which arises from the duplication formula of the elliptic functions. It is shown that ultradiscrete limit of the map and its solution yield the tent map and its solution simultaneously. A geometric interpretation of the dynamics of the tent map is given in terms of the tropical Jacobian of a certain tropical curve. Generalization to the maps corresponding to the $m$-th multiplication formula of the elliptic functions is also discussed.

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Kenji Kajiwara, Atsushi Nobe, Teruhisa Tsuda. 2008-03-31. Ultradiscretization of solvable one-dimensional chaotic maps. https://doi.org/10.1088/1751-8113/41/39/395202

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