Integrable mappings and the notion of anticonfinement

Takafumi Mase, Ralph Willox, Alfred Ramani, Basil Grammaticos

Published 2015-11-06Version 1

We examine the notion of anticonfinement in the context of the singularity analysis of discrete systems. A singularity is said to be anticonfined if singular values continue to arise indefinitely for the forwards and backwards iterations of the mapping, with only a finite number of iterates taking regular values in between. We show through several concrete examples that the behaviour of anticonfined singularities is strongly related to the integrability properties of such discrete mappings.