2017/04/25 by R. G. Halburd, Risto Korhonen, Halburd, R. G. +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1704.07927
openalex publication_date 2017/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A class of discrete equations is considered from three perspectives corresponding to three measures of the complexity of solutions: the (hyper-) order of meromorphic solutions in the sense of Nevanlinna, the degree growth of iterates over a function field and the height growth of iterates over the rational numbers. In each case, low complexity implies a form of singularity confinement which results in a known discrete Painlevé equation.