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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:nlin/0311014 (nlin)
[Submitted on 8 Nov 2003]

Title:Singularity confinement and algebraic integrability

Authors:S. Lafortune, A. Goriely
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Abstract: Two important notions of integrability for discrete mappings are algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved quantities whereas singularity confinement is associated with the local analysis of singularities. In this paper, the relationship between these two notions is explored for birational autonomous mappings. Two types of results are obtained: first, algebraically integrable mappings are shown to have the singularity confinement property. Second, a proof of the non-existence of algebraic conserved quantities of discrete systems based on the lack of confinement property is given.
Comments: 18 pages, no figure
Subjects: Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:nlin/0311014 [nlin.SI]
  (or arXiv:nlin/0311014v1 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.nlin/0311014
Related DOI: https://doi.org/10.1063/1.1640797

Submission history

From: Lafortune [view email]
[v1] Sat, 8 Nov 2003 23:05:52 UTC (21 KB)
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