Riemann Surfaces, Dynamics and Hyperbolic Geometry

黎曼曲面、动力学与双曲几何。McMullen DMS-9806424这个项目将研究几何结构和动力系统的分类，在设置中，允许对具体例子进行协调一致的研究。 它的范围包括迭代有理映射，Kleinian群，黎曼曲面上的投影结构，以及投影平面上的代数动力学。 重整化、谱理论与复动力学的相互作用以及Teichmuller理论在三维流形中的应用是主要的研究方向。 从气象学到机器人技术，动力系统的控制和预测在科学和技术中起着核心作用。 这个项目将包括计算机探索数学上简单的系统，表现出丰富的组合结构和普遍的分析功能。 其目的是推进动力学和几何的理论理解。

Riemann Surfaces, Dynamics and Hyperbolic Geometry-C. McMullen DMS-9806424 This project will study the classification of geometric structures and dynamical systems, in settings that allow for a concerted study of specific examples. Its scope includes iterated rational maps, Kleinian groups, projective structures on Riemann surfaces, and algebraic dynamics on the projective plane. Renormalization, the interaction of spectral theory with complex dynamics, and applications of Teichmuller theory to 3-manifolds are among the main research directions. From meteorology to robotics, the control and prediction of dynamical systems plays a central role in science and technology. This project will include computer explorations of mathematically simple systems that exhibit rich combinatorial structure and universal analytic features. Its aim is to advance the theoretical understanding of dynamics and geometry.