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

Kenji Kajiwara, Masanobu Kaneko, Atsushi Nobe, Teruhisa Tsuda

Research output: Contribution to journalArticle

4 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 languageEnglish
Pages (from-to)315-338
Number of pages24
JournalKyushu Journal of Mathematics
Volume63
Issue number2
DOIs
Publication statusPublished - Oct 30 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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