Integrable four-dimensional symplectic maps of standard type

Details Integrable four-dimensional symplectic maps of standard type Integrable four-dimensional symplectic maps of standard type

1993-04-28

arxiv.org/abs/solv-int/9304003v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

5 pages, compile with plain TEX. No figures. To appear in Physics Letters A

Scientific paper

10.1016/0375-9601(93)90027-W

We search for rational, four-dimensional maps of standard type (x_{n+1} -
2x_n + x_{n-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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