Diophantine Integrability

Details Diophantine Integrability Diophantine Integrability

2005-04-13

arxiv.org/abs/nlin/0504027v1

J. Phys. A: Math. Gen. 38 (2005) L263-L269

Nonlinear Sciences

Exactly Solvable and Integrable Systems

6 pages, 4 figures

Scientific paper

10.1088/0305-4470/38/16/L01

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.

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