Tropical geometric interpretation of ultradiscrete singularity confinement
Mathematical Physics
2013-01-31 v2 Dynamical Systems
math.MP
Abstract
Using the interpretation of the ultradiscretization procedure as a non-Archimedean valuation, we use results of tropical geometry to show how roots and poles manifest themselves in piece-wise linear systems as points of non-differentiability. This will allow us to demonstrate a correspondence between singularity confinement for discrete integrable systems and ultradiscrete singularity confinement for ultradiscrete integrable systems.
Keywords
Cite
@article{arxiv.0802.1959,
title = {Tropical geometric interpretation of ultradiscrete singularity confinement},
author = {Christopher M. Ormerod},
journal= {arXiv preprint arXiv:0802.1959},
year = {2013}
}
Comments
15 Pages, rewritten to also consider P{\Delta}Es