Description
Book SynopsisThis is the first textbook-type presentation of tropical value distribution theory. It provides a detailed introduction of the tropical version of the Nevanlinna theory, describing growth and value distribution analysis of continuous, piecewise linear functions on the real axis. The book also includes applications of this theory to ultra-discrete equations. Three appendices are given to compare the contents of the theory with the classical counterparts in complex analysis.Detailed presentation of the proofs makes the book accessible for lecture courses and independent studies at the graduate and post-doctoral level.
Table of ContentsTropical Polynomials, Rationals and Exponentials; Tropical Entire Functions; One-dimensional Tropical Nevanlinna Theory; Clunie and Mohon'ko Type Theorems; Tropical Holomorphic Curves; Representations of Tropical Periodic Functions; Applications to Ultra-Discrete Equations; Appendices: Classical Nevanlinna and Cartan Theories; Introduction to Ultra-Discrete Painleve Equations; Some Operators in Complex Analysis;
