Integrable Third-Order Mappings and their Growth Properties

    2001, Volume 6, Number 4, pp.  443-448

    Author(s): Lafortune S., Carstea A. S., Ramani A., Grammaticos B., Ohta Y.

    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 $n^N$.
    Citation: Lafortune S., Carstea A. S., Ramani A., Grammaticos B., Ohta Y., Integrable Third-Order Mappings and their Growth Properties, Regular and Chaotic Dynamics, 2001, Volume 6, Number 4, pp. 443-448

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