Tropical curve theory and integrable piecewise linear map

Details Tropical curve theory and integrable piecewise linear map Tropical curve theory and integrable piecewise linear map

2011-11-24

arxiv.org/abs/1111.5771v1

Physics

Mathematical Physics

18 pages

Scientific paper

We present applications of tropical geometry to some integrable piecewise-linear maps, based on the lecture given by one of the authors (R. I.) at the workshop "Tropical Geometry and Integrable Systems" (University of Glasgow, July 2011), and on some new results obtained afterward. After a brief review on tropical curve theory, we study the spectral curves and the isolevel sets of the tropical periodic Toda lattice and the periodic Box-ball system.

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