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

F.A. Haggar, G.B. Byrnes, G.R.W. Quispel and H.W. Capel

Physica A: Statistical Mechanics and its Applications, 1996, vol. 233, issue 1, 379-394

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.

Keywords: Difference equations; k-symplectic maps; k-Lie symmetries; k-integrals (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:233:y:1996:i:1:p:379-394

DOI: 10.1016/S0378-4371(96)00142-2

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