Singularity confinement for maps with the Laurent property
arXiv:nlin/0602007 · doi:10.1016/j.physleta.2006.09.078
Abstract
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.
13 pages; typos corrected; comments & references added; reformulation of theorem
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Cited by in corpus (7)
- Investigation into the role of the Laurent property in integrability
- Laurent Polynomials and Superintegrable Maps
- Some integrable maps and their Hirota bilinear forms
- Hankel determinant solutions to several discrete integrable systems and the Laurent Property
- Singularities of the discrete KdV equation and the Laurent property
- From integrable equations to Laurent recurrences
- Growth of Mahler measure and algebraic entropy of dynamics with the Laurent property