previous :: next

### Fixed points and periodic points of semiflows of holomorphic maps

Edoardo Vesentini
Source: Abstr. Appl. Anal. Volume 2003, Number 4 (2003), 217-260.

#### Abstract

Let $\phi$ 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 $\phi$ implies that $\phi$ 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 $\phi$ 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 $\phi$ 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.

First Page:
Primary Subjects: 17C65, 32M15
Secondary Subjects: 46G20
Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aaa/1050426016
Digital Object Identifier: doi:10.1155/S1085337503203109
Mathematical Reviews number (MathSciNet): MR1982092
Zentralblatt MATH identifier: 01883746

previous :: next