Integrability of one degree of freedom symplectic maps with polar singularities

Details Integrability of one degree of freedom symplectic maps with polar singularities Integrability of one degree of freedom symplectic maps with polar singularities

2005-03-21

arxiv.org/abs/nlin/0503042v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, 2 figures

Scientific paper

10.1143/JPSJ.75.064006

In this paper, we treat symplectic difference equations with one degree of freedom. For such cases, we resolve the relation between that the dynamics on the two dimensional phase space is reduced to on one dimensional level sets by a conserved quantity and that the dynamics is integrable, under some assumptions. The process which we introduce is related to interval exchange transformations.

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