Dynamics of rational symplectic mappings and difference Galois theory

Details Dynamics of rational symplectic mappings and difference Galois theory Dynamics of rational symplectic mappings and difference Galois theory

2008-03-27

arxiv.org/abs/0803.3951v1

International Mathematics Research Notices 2008, 23 (2008) 23 p.

Mathematics

Dynamical Systems

Scientific paper

10.1093/imrn/rnn103

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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