Abstract
For Γ a lattice in PU(2,1), the isometries of the 2-complex ball naturally extend to an action in : we prove that the limit set of this action coincides with the complement of the ball in the projective space. We prove that the action is ergodic with respect to a certain measure. Also, we study other kinds of actions: for instance we construct an action whose limit set is the entire , but is not minimal although it is algebraically mixing.
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