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Singularity confinement for maps with the Laurent property

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Feb 2007Embargo end date: 01 Feb 2006 English Publisher:Elsevier BVJournal:Physics Letters A, volume 361, pages 341-345 (issn: 0375-9601, Copyright policy )
Authors: Hone, A. N. W.;

doi: 10.1016/j.physleta.2006.09.078 , 10.48550/arxiv.nlin/0602007

arXiv: nlin/0602007

Singularity confinement for maps with the Laurent property

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

Related Organizations
Keywords

Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems, Exactly Solvable and Integrable Systems (nlin.SI)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
19
Top 10%
Top 10%
Top 10%
Green
bronze