Ultradiscretization of solvable one-dimensional chaotic maps

Details Ultradiscretization of solvable one-dimensional chaotic maps Ultradiscretization of solvable one-dimensional chaotic maps

2008-03-28

arxiv.org/abs/0803.4062v2

Nonlinear Sciences

Chaotic Dynamics

11 pages

Scientific paper

10.1088/1751-8113/41/39/395202

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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