TY - JOUR

T1 - An ultradiscrete integrable map arising from a pair of tropical elliptic pencils

AU - Nobe, Atsushi

N1 - Funding Information:
The author is grateful to two anonymous referees for their helpful comments and suggestions. This work was partially supported by Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science (JSPS) , Nos. 19740086 and 22740100 .

PY - 2011/11/14

Y1 - 2011/11/14

N2 - 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.

AB - 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.

KW - QRT map

KW - Tropical elliptic curve

KW - Ultradiscrete integrable system

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U2 - 10.1016/j.physleta.2011.10.010

DO - 10.1016/j.physleta.2011.10.010

M3 - Article

AN - SCOPUS:80455176840

SN - 0375-9601

VL - 375

SP - 4178

EP - 4182

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

IS - 47

ER -