Mathematical Sciences: Dynamics of Polynomial Diffeomorphisms

首席研究员将研究C^2多项式的动力学、二次微分和数值分析中使用的迭代方案。在此过程中，他将利用两个类比。第一个是C^2的多项式微分同态和C的映射的动力学行为之间的相似性，第二个是这些多项式和公理A微分同态之间的相似性。近年来，复杂平面的多项式映射和有理映射的计算机迭代生成了精细分形。当然，这些都是单个复变量的函数。首席研究员将扩展这一理论，包括两个复杂变量函数的迭代。

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.