Topological Dynamics in Real and Complex Systems

该提案涉及低维动力学的几个主题。PI计划研究叠层的拓扑动力学;特别是他想进一步发展生长树的动力学，并用它来研究Julia集顶点的行为。他还想考虑类的非解析平面地图的人类似的众所周知的结果多项式可以证明。他的其他研究方向涉及吸引力类的合理地图和进一步发展的旋转理论，研究共存的周期取决于他们的特点类似旋转数的圆地图的程度之一。动力系统理论提供了研究复杂系统的工具，例如复杂的确定性过程随时间的演化。在通信理论、统计物理学和化学动力学等其他科学中使用这些强大的工具有着丰富而杰出的传统。

The proposal deals with several topics in low-dimensionaldynamics. The PI plans to investigate the topological dynamicsof laminations; in particular he would like to further developthe dynamics of growing trees and use it to study the behaviorof the vertices of the Julia set. He also wants to consider classes of non-analytic plane maps for whom analogs of well-knownresults for polynomials can be proven. Other directions of hisresearch are related to attractos for classes of rational maps and to further developing the rotation theory which studies coexistence of cycles depending on their characteristics similarto rotation numbers for circle maps of degree one. The theory of dynamical systems gives tools to study complex systems, for example the evolution of a complicated deterministicprocess over time. There is a rich and distinguished tradition of using these powerful tools in other sciences like communication theory, statistical physics, and chemical kinetics.