Tropical Nevanlinna theory and second main theorem

TL;DR

This paper develops a tropical version of Nevanlinna theory for real-valued piecewise linear functions, including a second main theorem, with applications to ultra-discrete equations.

Contribution

It introduces a tropical Nevanlinna theory framework and proves a tropical second main theorem for the first time.

Findings

Established a tropical second main theorem.

Applied the theory to ultra-discrete equations.

Extended Nevanlinna theory to tropical, piecewise linear functions.

Abstract

We present a version of the tropical Nevanlinna theory for real-valued, continuous, piecewise linear functions on the real line. In particular, a tropical version of the second main theorem is proved. Applications to some ultra-discrete equations are given.