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

Kenji Kajiwara; Masanobu Kaneko; Atsushi Nobe; Teruhisa Tsuda

doi:10.2206/kyushujm.63.315

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

Kenji Kajiwara^*, Masanobu Kaneko, Atsushi Nobe, Teruhisa Tsuda

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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
Pages (from-to)	315-338
Number of pages	24
Journal	Kyushu Journal of Mathematics
Volume	63
Issue number	2
DOIs	https://doi.org/10.2206/kyushujm.63.315
Publication status	Published - 2009 Oct 30
Externally published	Yes

Keywords

Discrete dynamical systems
Plane cubic curve
Theta functions
Tropical geometry
Ultradiscretization

ASJC Scopus subject areas

Mathematics(all)

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10.2206/kyushujm.63.315

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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.'",

keywords = "Discrete dynamical systems, Plane cubic curve, Theta functions, Tropical geometry, Ultradiscretization",

author = "Kenji Kajiwara and Masanobu Kaneko and Atsushi Nobe and Teruhisa Tsuda",

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T1 - Ultradiscretization of a solvable two-dimensional chaotic map associated with the hesse cubic curve

AU - Kajiwara, Kenji

AU - Kaneko, Masanobu

AU - Nobe, Atsushi

AU - Tsuda, Teruhisa

PY - 2009/10/30

Y1 - 2009/10/30

N2 - 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.'

AB - 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.'

KW - Discrete dynamical systems

KW - Plane cubic curve

KW - Theta functions

KW - Tropical geometry

KW - Ultradiscretization

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JO - Kyushu Journal of Mathematics

JF - Kyushu Journal of Mathematics

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ER -

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

Abstract

Keywords

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