Basil Grammaticos ; Ralph Willox - Full-deautonomisation of a class of second-order mappings in ancillary form

ocnmp:10496 - Open Communications in Nonlinear Mathematical Physics, January 19, 2023, Volume 3 -
Full-deautonomisation of a class of second-order mappings in ancillary formArticle

Authors: Basil Grammaticos 1; Ralph Willox 2

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.

Volume: Volume 3
Published on: January 19, 2023
Accepted on: January 1, 2023
Submitted on: December 16, 2022
Keywords: integrable mappings singularity confinement deautonomisation integrability tests,integrable mappings,singularity confinement,deautonomisation,integrability tests,[NLIN]Nonlinear Sciences [physics]

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