English

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

R2 v1 2026-06-21T10:12:29.601Z