An ultradiscrete integrable map arising from a pair of tropical elliptic pencils
arXiv:1009.3997 · doi:10.1016/j.physleta.2011.10.010
Abstract
We present a tropical geometric description of a piecewise linear map whose invariant curve is a concave polygon. In contrast to convex polygons, a concave one is not directly related to tropical geometry; nevertheless the description is given in terms of the addition formula of a tropical elliptic curve. We show that the map is arising from a pair of tropical elliptic pencils each member of which is the invariant curve of the ultradiscrete QRT map.
14 pages, 4 figures