Three approaches to detecting discrete integrability
arXiv:1704.07927
Abstract
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.
12 pages