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 arises from a pair of tropical elliptic pencils, each member of which is the invariant curve of an ultradiscrete QRT map.
|ジャーナル||Physics Letters, Section A: General, Atomic and Solid State Physics|
|出版ステータス||Published - 2011 11月 14|
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