Linearisable Mappings and the Low-Growth Criterion

Details Linearisable Mappings and the Low-Growth Criterion Linearisable Mappings and the Low-Growth Criterion

2001-04-06

arxiv.org/abs/nlin/0104015v1

Journ. Phys. A 33, L287-L292 (2000)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

9 pages, no figure

Scientific paper

10.1088/0305-4470/33/31/104

We examine a family of discrete second-order systems which are integrable through reduction to a linear system. These systems were previously identified using the singularity confinement criterion. Here we analyse them using the more stringent criterion of nonexponential growth of the degrees of the iterates. We show that the linearisable mappings are characterised by a very special degree growth. The ones linearisable by reduction to projective systems exhibit zero growth, i.e. they behave like linear systems, while the remaining ones (derivatives of Riccati, Gambier mapping) lead to linear growth. This feature may well serve as a detector of integrability through linearisation.

Affiliated with

Also associated with

No associations

Rating

Linearisable Mappings and the Low-Growth Criterion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Linearisable Mappings and the Low-Growth Criterion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Linearisable Mappings and the Low-Growth Criterion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-657259