Fixed points and periodic points of semiflows of holomorphic maps

[摘要] Letϕbe a semiflow of holomorphic maps of a bounded domainDin a complex Banach space. The general question arises underwhich conditions the existence ofa periodic orbit ofϕimplies thatϕitself is periodic. An answer is provided, in the first part of this paper, in the case in whichDis the open unit ball of aJ∗-algebra andϕacts isometrically. More precise results are provided when theJ∗-algebra is a Cartan factor of type one ora spin factor. The second part of this paper deals essentially with the discrete semiflowϕgenerated by the iterates of a holomorphic map. It investigateshow the existence of fixed points determines the asymptotic behaviour of the semiflow. Some of these results are extended to continuous semiflows.

[学科分类] 数学（综合）