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在变量的平滑变化下可以被认为是等价的。这是一个很自然的问题，因为动力学的结果在变量变化时应该是不变的。该问题还涉及奇异理论（将函数分类到域和值域变量的光滑变化）、动力系统的拓扑分类和群作用分类的刚性规划。我们将讨论以下情况，当一个合理的分类可以完成：a)双曲不动点附近的局部等价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，并试图向人们介绍这一研究领域。日期：2001年6月4日至8日。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