Integrable four-dimensional symplectic maps of standard type
solv-int
2009-10-22 v1 Exactly Solvable and Integrable Systems
Abstract
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.
Cite
@article{arxiv.solv-int/9304003,
title = {Integrable four-dimensional symplectic maps of standard type},
author = {Robert I. McLachlan},
journal= {arXiv preprint arXiv:solv-int/9304003},
year = {2009}
}
Comments
5 pages, compile with plain TEX. No figures. To appear in Physics Letters A