Commuting Time Evolutions in the Tropical Periodic Toda Lattice

Abstract

The tropical (ultradiscrete) periodic Toda lattice is a dynamical system derived from a time-discretized version of the periodic Toda lattice through a limiting procedure called tropicalization. We propose a new formulation for this dynamical system with a representation by two-colored strips. Based on this formulation, a family of its commuting time evolutions is constructed.

arXiv comment16 pages

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Cited by in corpus (2)

• Invariant measures for the box-ball system based on stationary Markov chains and periodic Gibbs measures
• Combinatorial aspects of the conserved quantities of the tropical periodic Toda lattice