NSF/CBMS Regional Conference in the Mathematical Sciences - Equivalence of dynamical systems under smooth changes of variables and rigidity - Summer 2001

我们将讨论当两个动力系统可以被认为是等价的变量的光滑变化。这是一个自然的问题，因为动力学的结果应该在变量变化下保持不变。 这个问题也与奇点理论有关（直到定义域和值域的变量的平滑变化的分类函数）、动力系统的拓扑分类和群作用分类的刚性程序。我们将讨论以下情况，当可以实现合理的分类时：a）双曲不动点附近的局部等价性B）双曲系统c）KAM理论d）幂零群e）重整化。讲座将是教学性的，并将试图向人们介绍这一领域的研究。日期：6月4日至8日，2001.http://www.math.missouri.edu/~staff/conference/cbms-conf.html

We will discuss when two dynamical systems can be considered equivalent under a smooth change of variables. This is a natural problem since results on dynamics should be invariant under changes of variables. The problem is also related to singularity theory (classifying functions up to smooth changes of variables of the domain and the range), the topological classification of dynamical systems, and the rigidity program of classification of group actions.We will discuss the following situations, when a reasonable classification can be accomplished:a) Local equivalence near a hyperbolic fixed point b) Hyperbolic systems c) KAM theory d) Nilpotent groups e) Renormalization.The lectures will be pedagogical and will attempt to introduce people to this area of research.Dates: June 4-8, 2001.http://www.math.missouri.edu/~staff/conference/cbms-conf.html