Abstract

The six Painlev\’e equations play an important role in many areas of mathematics and physics, and the connection with integrable systems has been well-established. Recently, discrete integrable systems have gained more attention and hence it is natural to consider discrete versions of Painlevé equations. In this talk, we will present discrete forms of the , and . These mappings go over to the Painlev\’e equations in the continuous limit. The singularity confinement test as a discrete analogue of the Painlevé property will be also discussed.