Folding Transformations and HKY Mappings

DOI

10.1142/S1402925111001179How to use a DOI?

Keywords

Integrable mapping; invariant; QRT mapping; HKY mapping; folding transformation; elliptic functions; discrete Painlevé equations

Abstract

We present a new method for the derivation of mappings of HKY type. These are second-order mappings which do not have a biquadratic invariant like the QRT mappings, but rather an invariant of degree higher than two in at least one of the variables. Our method is based on folding transformations which exist for some discrete Painlevé equations. They are transformations which relate the variable of a discrete Painlevé equation to the square of the variable of some other one. By considering the autonomous limit of these relations we derive folding-like transformations which relate QRT mappings to HKY ones. We construct the invariants of the latter mappings and show how they can be extended beyond the ones given by the strict application of the folding transformation.

Copyright

© 2011 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - B. Grammaticos
AU  - A. Ramani
AU  - R. Willox
PY  - 2021
DA  - 2021/01/07
TI  - Folding Transformations and HKY Mappings
JO  - Journal of Nonlinear Mathematical Physics
SP  - 75
EP  - 85
VL  - 18
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001179
DO  - 10.1142/S1402925111001179
ID  - Grammaticos2021
ER  -