Integrable third-order mappings and their growth properties (Q1860531)

The authors study the degree growth of the iterates of the initial conditions for a class of third-order integrable mappings which result from the coupling of a discrete Painlevé equation to a homographic method. They show that the degree grows like \(n^3\). In the special cases where the mapping satisfies a singularity confinement requirement they find a slower, quadratic growth. Finally they present a method for the construction of integrable \(N\)th-order mappings with degree growth \(n^N\).