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26 February 2003 Fixed points and periodic points of semiflows of holomorphic maps
Edoardo Vesentini
Abstr. Appl. Anal. 2003(4): 217-260 (26 February 2003). DOI: 10.1155/S1085337503203109


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.


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Edoardo Vesentini. "Fixed points and periodic points of semiflows of holomorphic maps." Abstr. Appl. Anal. 2003 (4) 217 - 260, 26 February 2003.


Published: 26 February 2003
First available in Project Euclid: 15 April 2003

zbMATH: 1106.47303
MathSciNet: MR1982092
Digital Object Identifier: 10.1155/S1085337503203109

Primary: 17C65 , 32M15
Secondary: 46G20

Rights: Copyright © 2003 Hindawi

Vol.2003 • No. 4 • 26 February 2003
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