Fixed points and periodic points of semiflows of holomorphic maps
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.
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