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

✍ Scribed by F.A. Haggar; G.B. Byrnes; G.R.W. Quispel; H.W. Capel

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 572 KB
Volume: 233
Category: Article
ISSN: 0378-4371
DOI: 10.1016/s0378-4371(96)00142-2

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✦ Synopsis

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.

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