Dynamics on Two-Dimensional Surfaces

这是一个研究低维动力系统的建议。最重要的长期项目是更好地理解C^r类属区域的拓扑描述，其中r 1。 此外，proposer希望调查的行动，更一般的群体比整数或reals的表面上，特别是面积保持actions.Professor弗兰克斯将继续他的调查thedynamics的表面maps。 对这类变换的研究，特别是保面积变换的研究，有着悠久的历史，可以追溯到Poincare和G。D.伯克霍夫 这一领域的结果在经典力学和更现代的混沌动力学中有许多应用。 该研究将解决二维离散动力系统中存在周期性行为的问题，并对此类系统的动力学进行拓扑描述。

This is a proposal to investigate aspects of low dimensional dynamicalsystems. The most important long term project is to betterunderstand a topological description of C^r generic area preservingdiffeomorphisms of surfaces where r 1. In addition the proposerhopes to investigate the action of more general groups than the integers or the reals on surfaces, and in particular area preserving actions.Professor Franks will continue his investigation of thedynamics of surface maps. The study of such transformations,especially area preserving ones, has a long history going back toPoincare and G. D. Birkhoff. There are numerous applications ofresults in this area to classical mechanics as well as more modernchaotic dynamics. The proposed research will address questionsconcerning the existence of periodic behavior in area preservingtwo-dimensional discrete dynamical systems and a topologicaldescription of the dynamics of such systems.