Singularity confinement and algebraic integrability

Details Singularity confinement and algebraic integrability Singularity confinement and algebraic integrability

2003-11-08

arxiv.org/abs/nlin/0311014v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages, no figure

Scientific paper

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.

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