English

Diophantine Integrability

Exactly Solvable and Integrable Systems 2009-11-11 v1

Abstract

The heights of iterates of the discrete Painleve equations over number fields appear to grow no faster than polynomials while the heights of generic solutions of non-integrable discrete equations grow exponentially. This gives rise to a simple and effective numerical test for the integrability of discrete equations. Numerical evidence and theoretical results are presented. Connections with other tests for integrability and Vojta's dictionary are discussed.

Keywords

Cite

@article{arxiv.nlin/0504027,
  title  = {Diophantine Integrability},
  author = {R. G. Halburd},
  journal= {arXiv preprint arXiv:nlin/0504027},
  year   = {2009}
}

Comments

6 pages, 4 figures