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arXiv · 1412.5686

The redemption of singularity confinement

Alfred Ramani·Basil Grammaticos·Ralph Willox·Takafumi Mase·Masataka Kanki
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Abstract

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 Hietarinta-Viallet, 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.

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Alfred Ramani, Basil Grammaticos, Ralph Willox, Takafumi Mase, Masataka Kanki. 2014-12-18. The redemption of singularity confinement. https://doi.org/10.1088/1751-8113/48/11/11ft02

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