Degenerations of maximal representations, non-Archimedean upper half space and laminations

We study degenerations of maximal representations into Sp(2n,R) and identify phenomena already present in the Thurston boundary of Teichmüller apace as well as new geometric features.  We give equivalent conditions for the existence of measured laminations in term of an appropriate notino of length.  This is joint work with Marc Burger, Anne Parreau and Beatrice Pozzetti.