Ultradiscretization of a solvable two-dimensional chaotic map associated with the Hesse cubic curve

Details Ultradiscretization of a solvable two-dimensional chaotic map associated with the Hesse cubic curve Ultradiscretization of a solvable two-dimensional chaotic map associated with the Hesse cubic curve

2009-03-02

arxiv.org/abs/0903.0331v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

24 pages, to appear in Kyushu J. Math.(2009). v2: Introduction modified, some references added and typos corrected

Scientific paper

We present a solvable two-dimensional piecewise linear chaotic map which arises from the duplication map of a certain tropical cubic curve. Its general solution is constructed by means of the ultradiscrete theta function. We show that the map is derived by the ultradiscretization of the duplication map associated with the Hesse cubic curve. We also show that it is possible to obtain the nontrivial ultradiscrete limit of the solution in spite of a problem known as "the minus-sign problem."

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