How to detect the integrability of discrete systems

International audienceSeveral integrability tests for discrete equations will be reviewed. All tests considered can be applied directly to a given discrete equation and do not rely on the a priori knowledge of the existence of related structures such as Lax pairs. Specifically, singularity confinement, algebraic entropy, Nevanlinna theory, Diophantine integrability and discrete systems over finite fields will be described