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We examine the notion of anticonfinement and the role it has to play in thesingularity analysis of discrete systems. A singularity is said to beanticonfined if singular values continue to arise indefinitely for the forwardand backward iterations of a mapping, with only a finite number of iteratestaking regular values in between. We show through several concrete examplesthat the behaviour of some anticonfined singularities is strongly related tothe integrability properties of the discrete mappings in which they arise, andwe explain how to use this information to decide on the integrability ornon-integrability of the mapping.

Integrable mappings and the notion of anticonfinement