Integrable four-dimensional symplectic maps of standard type
Robert I. McLachlan
Abstract
We search for rational, four-dimensional maps of standard type (xn+1 - 2xn + xn-1 = eps f(x,eps)) possessing one or two polynomial integrals. There are no non-trivial maps corresponding to cubic oscillators, but we find a four-parameter family of such maps corresponding to quartic oscillators. This seems to be the only such example.
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