An ultradiscrete integrable map arising from a pair of tropical elliptic pencils

Details An ultradiscrete integrable map arising from a pair of tropical elliptic pencils An ultradiscrete integrable map arising from a pair of tropical elliptic pencils

2010-09-21

arxiv.org/abs/1009.3997v1

Physics Letters A 375 (2011) pp. 4178-4182

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages, 4 figures

Scientific paper

10.1016/j.physleta.2011.10.010

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.

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