arXiv 0803.40622008-03-31nlin.CDmath.DSnlin.SI

Ultradiscretization of solvable one-dimensional chaotic maps

Kenji Kajiwara, Atsushi Nobe, Teruhisa Tsuda

备注：: 11 pages
DOI：: 10.1088/1751-8113/41/39/395202

英文摘要：

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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