Mathematical Sciences: Complex Analysis

三位首席研究员将继续研究Teichmuller空间、黎曼曲面族和复平面动力系统之间的关系。特别注意的是三度Mandelbrot集合的中心多项式和Julia集合是康托尔。Douady-Earle质心坐标的工作将继续进行。本文将研究三次多项式的精细分形Julia集和广义Mandelbrot集。这些可以用家用电脑上的简单程序生成的集合最近引起了公众对数学的兴趣。首席研究员将继续研究这些分形的深层数学性质。

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.