0802.1959 (Christopher M. Ormerod)

Tropical geometric interpretation of ultradiscrete singularity
confinement    [PDF]

Christopher M. Ormerod

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.

View original: http://arxiv.org/abs/0802.1959