International Conference on Applied Mathematics & Computer Science

Prof. Dorin Ghisa

York University, Glendon College, Department of Mathematics, 2275-Bayview Avenue
Toronto, Canada

Title of the paper: Conformal Self Mappings of the Fundamental Domains of Analytic Functions

Abstract: Conformal self mappings of a given domain of the complex plane can be obtained by using the Riemann Mapping Theorem in the following way. Two different conformal mappings φ and ψ of that domain onto one of the standard domains: the unit disc, the complex plane or the Riemann sphere are taken and then ψ^-1°φ is what we are looking for. Yet, this is just a theoretical construction, since the Riemann Mapping Theorem does not offer any concrete expression of those functions. The Möbius transformations are concrete, but they can be used only for particular circular domains. We are proving in this paper that conformal self mappings of any fundamental domain of an arbitrary analytic function can be obtained via Möbius transformations as long as we allow that domain to have slits. Moreover, those mappings enjoy group properties. Graphic illustrations are offered for the most familiar analytic functions.

Bio: Dorin Ghisa Born in 1940 in Romania. Graduated in 1963 with a degree in Mathematics from the University Babes-Bolyai, Cluj. PhD. In Mathematics at the University of Bucharest in 1975. Assistant Professor and Associate Professor at the University of Timisoara 1963-1976. Professor at the University of Science and Technology, Algiers, Algeria 1976-1980. University of Montreal, Canada 1980-1981. University of Moncton, Canada 1981-1984 York University, Toronto, Canada from 1984 until retirement and affiliated to it until today. Emeritus member of the AMS from 2000.