Dynamics in One Complex Variable
by John Milnor
Publisher: Princeton University Press 1991
Number of pages: 146
This volume studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology.
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by Christian Berg - Kobenhavns Universitet
Contents: Holomorphic functions; Contour integrals and primitives; The theorems of Cauchy; Applications of Cauchy's integral formula; Zeros and isolated singularities; The calculus of residues; The maximum modulus principle; Moebius transformations.
by Georges Valiron - Chelsea Pub. Co.
These lectures give us, in the form of a number of elegant and illuminating theorems, the latest word of mathematical science on the subject of Integral Functions. They descend to details, they take us into the workshop of the working mathematician.
by S. Axler, J. McCarthy, D. Sarason - Cambridge University Press
This volume consists of expository articles on holomorphic spaces. Topics covered are Hardy spaces, Bergman spaces, Dirichlet spaces, Hankel and Toeplitz operators, and a sampling of the role these objects play in modern analysis.
by H. Maass - Tata institute of Fundamental Research
This is an elementary introduction to the theory of modular functions and modular forms. Basic facts from the theory of functions of a complex variable and some properties of the elementary transcendental functions are the only prerequisites.