Linearisable mappings, revisited

DOI

10.1080/14029251.2016.1237196How to use a DOI?

Keywords

linearisation; Gambier mapping; degree growth; anticonfinement

Abstract

We examine the growth properties of second-order mappings which are integrable by linearisation and which generically exhibit a linear growth of the homogeneous degree of initial conditions. We show that for Gambier-type mappings for which the growth proceeds generically with a step of 1 there exist cases where the degree increase by unity every two steps. We examine also mappings belonging to the family known as “of third kind” in relation to the approach of Diller and Favre concerning the regularisable or not character of mappings and show that the anticonfined singularities of these mappings exhibit a linear growth with step 1. (The term anticonfined is used for singularities where the singular values extend all the way to infinity on both sides with just a few regular values in the middle). Moreover we construct specific examples of Gambier-type mappings which have anticonfined singularities and where the degree of the singularity increases linearly but where the average slope can be adjusted so as to be arbitrarily small.

Copyright

© 2016 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  - J. Satsuma
PY  - 2021
DA  - 2021/01/06
TI  - Linearisable mappings, revisited
JO  - Journal of Nonlinear Mathematical Physics
SP  - 466
EP  - 473
VL  - 23
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2016.1237196
DO  - 10.1080/14029251.2016.1237196
ID  - Grammaticos2021
ER  -