Fixed points and periodic points of semiflows of holomorphic maps

Edoardo Vesentini

Abstract and Applied Analysis, 2003, vol. 2003, 1-44

Abstract:

Let ϕ be a semiflow of holomorphic maps of a bounded domain D in a complex Banach space. The general question arises under which conditions the existence of a periodic orbit of ϕ implies that ϕ itself is periodic. An answer is provided, in the first part of this paper, in the case in which D is the open unit ball of a J ∗ -algebra and ϕ acts isometrically. More precise results are provided when the J ∗ -algebra is a Cartan factor of type one or a spin factor. The second part of this paper deals essentially with the discrete semiflow ϕ 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.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:619876

DOI: 10.1155/S1085337503203109

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