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

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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 arises from a pair of tropical elliptic pencils, each member of which is the invariant curve of an ultradiscrete QRT map.

Original languageEnglish
Pages (from-to)4178-4182
Number of pages5
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume375
Issue number47
DOIs
Publication statusPublished - 2011 Nov 14
Externally publishedYes

Keywords

  • QRT map
  • Tropical elliptic curve
  • Ultradiscrete integrable system

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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