### 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 the 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 mth multiplication formula of the elliptic functions is also discussed.

Original language | English |
---|---|

Article number | 395202 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 41 |

Issue number | 39 |

DOIs | |

Publication status | Published - Oct 3 2008 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

## Fingerprint Dive into the research topics of 'Ultradiscretization of solvable one-dimensional chaotic maps'. Together they form a unique fingerprint.

## Cite this

Kajiwara, K., Nobe, A., & Tsuda, T. (2008). Ultradiscretization of solvable one-dimensional chaotic maps.

*Journal of Physics A: Mathematical and Theoretical*,*41*(39), [395202]. https://doi.org/10.1088/1751-8113/41/39/395202