Mathematical Sciences: Problems in Complex Analysis

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9505149 Fornaess The proposed research lies in the area of several complex variables. Complex dynamical systems in several variables - this is a new area of research founded by the proposer and his coworkers - will be pursued: iteration of holomorphic maps, holomorphic flows, and holomorphic hulls are among the topics of study in this area. The Cauchy-Riemann operator in singular spaces and the boundary regularity of holomorphic mappings will also be investigated. Complex dynamical systems generalize real dynamical systems arising from autonomous systems of ordinary differential equations. Real dynamical systems are widely used to model natural phenomena including fluid flow, planetary motion, and ecological systems. Complex dynamical systems, which are relatively recent constructs, have already found applications in fractal geometry.