Integrability of Discrete-Time Systems

  • B. Grammaticos
  • G. Karra
  • V. Papageorgiou
  • A. Ramani
Part of the NATO ASI Series book series (NSSB, volume 298)

Abstract

A new integrability criterion for discrete-time systems, based on the notion of the confinement of the singularities that may appear in rational mappings is presented. Discrete analogues of the Painlevé equations are derived as second-order, nonautonomous mappings, with the help of this integrability detector. Moreover a parallel between continuous and discrete systems is established by showing that to each kind of “continuous” integrability there exists a “discrete” analogue.

Key words

Integrability Discrete-time systems Mappings Painlevé equations Singularity confinement Linearizable mappings 

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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • B. Grammaticos
    • 1
  • G. Karra
    • 1
  • V. Papageorgiou
    • 2
  • A. Ramani
    • 3
  1. 1.LPN, Univ. Paris VIIParisFrance
  2. 2.Dept. of Mathematics and Computer Science and Institute for Nonlinear StudiesClarkson UniversityPotsdamUSA
  3. 3.CPT, Ecole PolytechniquePalaiseauFrance

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