Mathematical Sciences: Dynamics of Polynomial Diffeomorphisms

首席研究员将研究 C^2多项式、二次微分和迭代 用于数值分析的方案。 他会利用 两个类比。 第一个是 C^2和C^3的多项式同态的动力学行为 C的地图。 第二点是 在这些相同的多项式和公理A之间。 近年来，精致的分形已经产生了 复形的多项式和有理映射的计算机迭代 飞机 当然，这些都是一个单一的功能， 复变数 首席研究员将延长这一点 包含两个复变函数的迭代的理论 变量

The principal investigator will study the dynamics of polynomials of C^2, quadratic differentials, and iteration schemes used in numerical analysis. In doing so he will exploit two analogies. The first of these is the similarities between the dynamical behavior of polynomial diffeomorphisms of C^2 and that of maps of C. The second of these is the similarities between these same polynomials and Axiom A diffeomorphism. In recent years exquisite fractals have been generated by computer iteration of polynomial and rational maps of the complex plane. Of course, each of these were functions of a single complex variable. The principal investigator will extend this theory to include iteration of functions of two complex variables.