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arXiv · 0803.3951

Dynamics of rational symplectic mappings and difference Galois theory

Guy Casale·Julien Roques
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Abstract

In this paper we study the relationship between the integrability of rational symplectic maps and difference Galois theory. We present a Galoisian condition, of Morales-Ramis type, ensuring the non-integrability of a rational symplectic map in the non-commutative sense (Mishchenko-Fomenko). As a particular case, we obtain a com- plete discrete analogue of Morales-Ramis Theorems for non-integrabi- lity in the sense of Liouville.

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Guy Casale, Julien Roques. 2008-03-27. Dynamics of rational symplectic mappings and difference Galois theory. https://doi.org/10.1093/imrn%2Frnn103

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