P.O. Box 210089, Tuscon, AZ 85721
Department of Mathematics, University of Arizona
Lafortune S., Carstea A. S., Ramani A., Grammaticos B., Ohta Y.
Integrable Third-Order Mappings and their Growth Properties
2001, vol. 6, no. 4, pp. 443-448
We 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 an homographic mapping. We show that the degree grows like $n^3$. In the special cases where the mapping satisfies the singularity confinement requirement we find a slower, quadratic growth. Finally we present a method for the construction of integrable $N$th-order mappings with degree growth $n^N$.