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Article Dans Une Revue Open Communications in Nonlinear Mathematical Physics Année : 2023

Full-deautonomisation of a class of second-order mappings in ancillary form

Résumé

We present an application of the full-deautonomisation method to a class of secondorder mappings which, using an ancillary variable, can be cast into a form that greatly facilitates the study of their singularities. The ancillary approach was originally introduced to make it possible to construct discrete Painlevé equations associated with the affine Weyl group E (1) 8 by deautonomising a QRT mapping. The full-deautonomisation method has been shown to offer a practical technique for calculating the exact dynamical degree of a mapping, whereby allowing the detection of discrete integrability using only singularity analysis. We study the confinement property for a given singularity, for a wide class of mappings that includes the autonomous limit of the standard additive Painlevé equation with E (1) 8 symmetry. This leads to a class of non-autonomous mappings, which can be integrable or not, for which we obtain their exact dynamical degrees. The case of a non-confining singularity is also analysed and again we obtain the corresponding dynamical degrees.
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Dates et versions

hal-03898145 , version 1 (14-12-2022)
hal-03898145 , version 2 (11-01-2023)

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Basil Grammaticos, Ralph Willox. Full-deautonomisation of a class of second-order mappings in ancillary form. Open Communications in Nonlinear Mathematical Physics, 2023, Volume 3, pp.1-22. ⟨10.46298/ocnmp.10496⟩. ⟨hal-03898145v2⟩
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