### Abstract

We present a solvable two-dimensional piecewise linear chaotic map that 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 non-trivial ultradiscrete limit of the solution in spite of a problem known as 'the minus-sign problem.'

Original language | English |
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Pages (from-to) | 315-338 |

Number of pages | 24 |

Journal | Kyushu Journal of Mathematics |

Volume | 63 |

Issue number | 2 |

DOIs | |

Publication status | Published - Oct 30 2009 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Kajiwara, K., Kaneko, M., Nobe, A., & Tsuda, T. (2009). Ultradiscretization of a solvable two-dimensional chaotic map associated with the hesse cubic curve.

*Kyushu Journal of Mathematics*,*63*(2), 315-338. https://doi.org/10.2206/kyushujm.63.315