Ultradiscretization of solvable one-dimensional chaotic maps
Chaotic Dynamics
2009-11-13 v2 Dynamical Systems
Exactly Solvable and Integrable Systems
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 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 -th multiplication formula of the elliptic functions is also discussed.
Cite
@article{arxiv.0803.4062,
title = {Ultradiscretization of solvable one-dimensional chaotic maps},
author = {Kenji Kajiwara and Atsushi Nobe and Teruhisa Tsuda},
journal= {arXiv preprint arXiv:0803.4062},
year = {2009}
}
Comments
11 pages