The redemption of singularity confinement

A Ramani, B Grammaticos, R Willox, T Mase, M Kanki
2015 Journal of Physics A: Mathematical and Theoretical  
We present a novel way to apply the singularity confinement property as a discrete integrability criterion. We shall use what we call a full deautonomisation approach, which consists in treating the free parameters in the mapping as functions of the independent variable, applied to a mapping complemented with terms that are absent in the original mapping but which do not change the singularity structure. We shall show, on a host of examples including the well-known mapping of
more » ... that our approach offers a way to compute the algebraic entropy for these mappings exactly, thereby allowing one to distinguish between the integrable and non-integrable cases even when both have confined singularities.
doi:10.1088/1751-8113/48/11/11ft02 fatcat:s6gg4ch5ibflhcspcqtnxpd3wa