Chapter 6: Representations of tropical periodic functions

In this chapter, our key result is to giving a representation of tropical meromorphic, periodic functions in terms of certain elementary tropical meromorphic functions that have, essentially, a sawtooth waveform, with their width, height and inclination depending on two parameters. Before proceeding to this representation, we first make some simple observations concerning periodic functions in the tropical setting. Without restricting generality, we assume in this chapter that tropical meromorphic functions f under consideration here are of period 1, unless otherwise specified. Then, trivially, f satisfies the elementary equation y(x + 1) ⊘ y(x) = 0, that is, y(x + 1) − y(x) = 0.