Mathematical Sciences: Complex Analysis

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The three Principal Investigators will continue their studies of the relationships between Teichmuller spaces, families of Riemann surfaces, and the dynamical systems of the complex plane. Specific attention will be paid to the degree three Mandelbrot set for centered polynomials and Julia sets which are Cantor. Work on the Douady-Earle barycentric coordinates will continue. The exquisite fractal Julia and generalized Mandelbrot sets will be studied for degree three polynomials. These sets which can be generated by simple programs on home computers have recently excited the general public about mathematics. The Principal Investigators will continue to study the deep mathematical properties of these fractals.