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Regular and Chaotic Dynamics, 2001, Volume 6, Issue 4, Pages 443–448
DOI: https://doi.org/10.1070/RD2001v006n04ABEH000188 (Mi rcd856) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Integrable Third-Order Mappings and their Growth Properties

S. Lafortunea, A. S. Carsteab, A. Ramanib, B. Grammaticosc, Y. Ohtad

a Department of Mathematics, University of Arizona, 85721 Tucson AZ, USA
b CPT, Ecole Polytechnique, CNRS, UMR 7644, 91128 Palaiseau, France
c GMPIB, Universitè Paris VII, Tour 24-14, 5e étage, case 7021, 75251 Paris, France
d Information Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan
Citations (9)
DOI: https://doi.org/10.1070/RD2001v006n04ABEH000188
Abstract: 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 $n^N$.
Received: 05.08.2001
Bibliographic databases:
Document Type: Article
MSC: 58K20
Language: English
Citation: S. Lafortune, A. S. Carstea, A. Ramani, B. Grammaticos, Y. Ohta, “Integrable Third-Order Mappings and their Growth Properties”, Regul. Chaotic Dyn., 6:4 (2001), 443–448
Citation in format AMSBIB
\Bibitem{LafCarRam01}
\by S.~Lafortune, A. S. Carstea, A.~Ramani, B.~Grammaticos, Y. Ohta
\paper Integrable Third-Order Mappings and their Growth Properties
\jour Regul. Chaotic Dyn.
\yr 2001
\vol 6
\issue 4
\pages 443--448
\mathnet{http://mi.mathnet.ru/rcd856}
\crossref{https://doi.org/10.1070/RD2001v006n04ABEH000188}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1876535}
\zmath{https://zbmath.org/?q=an:1011.39017}
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    • This publication is cited in the following 9 articles:
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