Ultradiscretization of solvable one-dimensional chaotic maps

Kenji Kajiwara, Atsushi Nobe, Teruhisa Tsuda

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish
Article number395202
JournalJournal of Physics A: Mathematical and Theoretical
Volume41
Issue number39
DOIs
Publication statusPublished - Oct 3 2008

Fingerprint

Tent Map
One-dimensional Maps
Chaotic Map
Elliptic function
Duplication
elliptic functions
Multiplication
Curve
multiplication
curves
Generalization
Interpretation

All Science Journal Classification (ASJC) codes

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

Cite this

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

In: Journal of Physics A: Mathematical and Theoretical, Vol. 41, No. 39, 395202, 03.10.2008.

Research output: Contribution to journalArticle

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