Singularity confinement for maps with the Laurent property A

  • . N . W . Hone
  • Published 2006


The singularity confinement test is very useful for isolating integrable cases of discrete-time dynamical systems, but it does not provide a sufficient criterion for integrability. Quite recently a new property of the bilinear equations appearing in discrete soliton theory has been noticed: the iterates of such equations are Laurent polynomials in the initial data. A large class of non-integrable mappings of the plane are presented which both possess this Laurent property and have confined singularities. MSC2000 numbers: 11B37, 93C10, 93C55 There continues to be a great deal of interest in discrete-time dynamical systems that are integrable. There is a vast range of such systems, including symplectic maps and Bäcklund transformations for Hamiltonian systems in classical mechanics [1], mappings that preserve plane curves [2] which occur in statistical mechanics, discrete analogues of Painlevé transcendents [3], partial difference soliton equations appearing in numerical analysis and solvable quantum models [4], and equations arising in theories of discrete geometry and discrete analytic functions [5]. For some ∗Institute of Mathematics, Statistics & Actuarial Science, University of Kent, Canterbury CT2 7NF, United Kingdom

Cite this paper

@inproceedings{Hone2006SingularityCF, title={Singularity confinement for maps with the Laurent property A}, author={. N . W . Hone}, year={2006} }