A Jordan approach to iteration theory for bounded symmetric domains

We explore Denjoy-Wolff type results for a holomorphic fixed-point free map, f, on a finite dimensional bounded symmetric domain B. Jordan techniques allow us to replace the usual horospheres, defined in terms of the Kobayashi distance, by convex affine f-invariant subsets of B. We establish further properties of these subsets and, in addition, prove that all constant subsequential limits of (fⁿ) must lie in K<inf>ξ</inf>, the closure of the affine boundary component of the Wolff point ξ ∈ ∂B. In particular, if ξ is extreme then it is the only possible constant subsequential limit.