Appears in collection : 2018 - T1 - WS2 - Model theory and valued fields

A difference equation over an increasing transformal valued field is known to be analyzable over the residue field. This leads to a dynamical theory of equivalence of finite dimensional difference varieties, provided one knows that the residue field isstably embedded as a pure difference field. In characteristic zero this follows from work of Azgin’s. I will report on joint work with Yuval Dor, settling the question in positive characteristic.