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Fixed points and periodic points of semiflows of holomorphic maps

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  • Edoardo Vesentini

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.

Suggested Citation

  • Edoardo Vesentini, 2003. "Fixed points and periodic points of semiflows of holomorphic maps," Abstract and Applied Analysis, Hindawi, vol. 2003, pages 1-44, January.
    • Handle: RePEc:hin:jnlaaa:619876
    DOI: 10.1155/S1085337503203109
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