Singularity confinement and algebraic integrability.

Two important notions of integrability for discrete mappings, algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved quantities and singularity confinement is associated with the local analysis of singularities. In this article, the relationship between these two notions is explored for birational autonomous mappings. The main result of this article is that algebraically integrable mappings are shown to have the singularity confinement property. Using this result, the proof of the nonexistence of algebraic conserved quantities for a class of discrete systems is given. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]