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

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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Year of publication:	1996
Authors:	Haggar, F.A. ; Byrnes, G.B. ; Quispel, G.R.W. ; Capel, H.W.
Published in:	Physica A: Statistical Mechanics and its Applications. - Elsevier, ISSN 0378-4371. - Vol. 233.1996, 1, p. 379-394
Publisher:	Elsevier
Subject:	Difference equations \| k-symplectic maps \| k-Lie symmetries \| k-integrals

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011058653