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k-integrals and k-Lie symmetries in discrete dynamical systems

Author

Listed:
  • Haggar, F.A.
  • Byrnes, G.B.
  • Quispel, G.R.W.
  • Capel, H.W.

Abstract

We generalize the concept of symplectic maps to that of k- symplectic maps: maps whose kth iterates are symplectic. Similarly, k-symmetries and k-integrals are symmetries (resp. integrals) of the kth iterate of the map. It is shown that k-symmetries and k-integrals are related by the k-symplectic structure, as in the k = 1 continuous case (Noether's theorem). Examples are given of k-integrals and their related k-symmetries for k = 1,…,4.

Suggested Citation

  • Haggar, F.A. & Byrnes, G.B. & Quispel, G.R.W. & Capel, H.W., 1996. "k-integrals and k-Lie symmetries in discrete dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 233(1), pages 379-394.
    • Handle: RePEc:eee:phsmap:v:233:y:1996:i:1:p:379-394
    DOI: 10.1016/S0378-4371(96)00142-2
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    References listed on IDEAS

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    1. Quispel, G.R.W. & Nijhoff, F.W. & Capel, H.W. & Van Der Linden, J., 1984. "Linear integral equations and nonlinear difference-difference equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 125(2), pages 344-380.
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