Edoardo Vesentini, "Fixed points and periodic points of semiflows of holomorphic maps", Abstract and Applied Analysis, vol. 2003, Article ID 619876, 44 pages, 2003. https://doi.org/10.1155/S1085337503203109
Fixed points and periodic points of semiflows of holomorphic maps
Let be a semiflow of holomorphic maps of a bounded domain in a complex Banach space. The general question arises under which conditions the existence of a periodic orbit of implies that itself is periodic. An answer is provided, in the first part of this paper, in the case in which is the open unit ball of a -algebra and acts isometrically. More precise results are provided when the -algebra is a Cartan factor of type one or a spin factor. The second part of this paper deals essentially with the discrete semiflow generated by the iterates of a holomorphic map. It investigates how the existence of fixed points determines the asymptotic behaviour of the semiflow. Some of these results are extended to continuous semiflows.
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