We discuss a few new results in the area of complex dynamics in higher dimension. We investigate generic properties of orbits of biholo-morphic symplectomorphisms of n. In particular we show (Corollary 3.4) that for a dense G δ set of maps, the set of points with bounded orbit has empty interior while the set of points with recurrent orbits nevertheless has full measure. We also investigate the space of real symplectomorphisms of Ê n which extend to n. For this space we show (Theorem 3.10) that for a dense G δ set of maps, the set of points with bounded orbit is an Fσ with empty interior.

No abstract

No abstract

No abstract

No abstract