Dynamics of rational symplectic mappings and difference Galois theory

Guy Casale (1) , Julien Roques (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 DMA - Département de Mathématiques et Applications - ENS Paris

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.

Domaines: Systèmes dynamiques [math.DS]

Guy Casale, Julien Roques. Dynamics of rational symplectic mappings and difference Galois theory. International Mathematics Research Notices, 2008, 2008 (23), 23 p. ⟨10.1093/imrn/rnn103⟩. ⟨hal-00267362⟩