Singularity confinement and algebraic integrability

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.

18 pages, no figure

References in corpus (1)

• Superintegrability with third order invariants in quantum and classical mechanics

Cited by in corpus (6)

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• The dynamical degree of billiards in an algebraic curve
• Derivation of Higher Dimensional Periodic Recurrence Equations by Nested Structure of Complex Numbers
• Complete integrable systems with unconfined singularities