Singularity confinement for maps with the Laurent property

Details Singularity confinement for maps with the Laurent property Singularity confinement for maps with the Laurent property

2006-02-03

arxiv.org/abs/nlin/0602007v4

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages; typos corrected; comments & references added; reformulation of theorem

Scientific paper

10.1016/j.physleta.2006.09.078

The singularity confinement test is very useful for isolating integrable cases of discrete-time dynamical systems, but it does not provide a sufficient criterion for integrability. Quite recently a new property of the bilinear equations appearing in discrete soliton theory has been noticed: the iterates of such equations are Laurent polynomials in the initial data. A large class of non-integrable mappings of the plane are presented which both possess this Laurent property and have confined singularities.

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