### 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 |
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Article number | 395202 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 41 |

Issue number | 39 |

DOIs | |

Publication status | Published - Oct 3 2008 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*41*(39), [395202]. https://doi.org/10.1088/1751-8113/41/39/395202

**Ultradiscretization of solvable one-dimensional chaotic maps.** / Kajiwara, Kenji; Nobe, Atsushi; Tsuda, Teruhisa.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 41, no. 39, 395202. https://doi.org/10.1088/1751-8113/41/39/395202

}

TY - JOUR

T1 - Ultradiscretization of solvable one-dimensional chaotic maps

AU - Kajiwara, Kenji

AU - Nobe, Atsushi

AU - Tsuda, Teruhisa

PY - 2008/10/3

Y1 - 2008/10/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=54749105110&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=54749105110&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/41/39/395202

DO - 10.1088/1751-8113/41/39/395202

M3 - Article

VL - 41

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 39

M1 - 395202

ER -