Iteration of holomorphic maps on Lie balls

We investigate iterations of fixed-point free holomorphic self-maps on a Lie ball of any dimension, where a Lie ball is a bounded symmetric domain and the open unit ball of a spin factor which can be infinite dimensional. We describe the invariant domains of a holomorphic self-map f on a Lie ball D when f is fixed-point free and compact, and show that each limit function of the iterates (f(n)) has values in a one-dimensional disc on the boundary of D. We show that the Mobius transformation g(a) induced by a nonzero element a in D may fail the Denjoy-Wolff-type theorem, even in finite dimension. We determine those which satisfy the theorem. (C) 2014 Elsevier Inc. All rights reserved.