Iteration of self-maps on a product of Hilbert balls

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:411

Article

Chu, Cho-Ho¹  Rigby, Michael¹ 

[1] Univ London, Sch Math Sci, London E1 4NS, England

关键词: Iteration;    Hilbert ball;    Polydisc;    Kobayashi distance;    JB*-triple;   

DOI  :  10.1016/j.jmaa.2013.10.009

来源: Elsevier

【 摘 要 】

Let D = D-1 x ... x D-p be a product of Hilbert balls, with coordinate maps pi(J) :(D) over bar -> (D) over bar (j): on the closure (D) over bar, for j = 1,..., p. Let f be a fixed-point free self-map on D, which is nonexpansive in the Kobayashi distance, and compact for p >=. 2. We describe the horospheres invariant under f and show that there exist a boundary point (xi(1),..., xi(p)) of D and a nonempty set J c {1,..., p} such that each limit function h of the iterates (f(n)) satisfies xi(j) is an element of pi(j) o h(D) for all j E J and pi(j) o h(.) = xi(j) whenever pi(J) o h(D) meets the boundary of D-j. For a single Hilbert ball D-1, either lim inf(n ->infinity) parallel to f(2n) (0)parallel to < 1 or (f(n)) converges locally uniformly to a constant map taking value at the boundary of D-1. (C) 2013 Elsevier Inc. All rights reserved.

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