Mathematical Sciences: Undergraduate Research in Analysis and Dynamical System

该奖项支持两名本科生在首席研究员的指导下研究数学分析和动力系统中的问题。分析的工作集中在与连续函数类有关的几何问题上。具体地说，学生将考虑连续函数的作文以及通过形成作文的凸组合而得到的结构。这项工作用马尔可夫算子研究中出现的保测量变换的组合来扩展早期的研究。对动力系统的研究将集中在最近发展的伪轨道跟踪思想上。阴影测量的是附近轨道可以追踪到的程度。这一现象很重要，因为具有跟踪特性的动力系统可以在计算机上建模。将鼓励学生在专业会议上展示他们的工作成果。

This award supports two undergraduates working under the direction of the principal investigator on problems in mathematical analysis and dynamical systems. The work in analysis centers on geometric questions related to classes of continuous functions. Specifically, the students will consider compositions of continuous function and the structures one obtains by forming convex combinations of the compositions. The work expands earlier investigations with combinations of measure preserving transformations which occurs in the study of Markov operators. Investigations into dynamical systems will focus on recently developed ideas of pseudo-orbit shadowing. Shadowing measures the degree to which an orbit can be traced by nearby orbits. The phenomenon is important because dynamical systems with the shadowing property can be modeled on a computer. Students will be encouraged to present the results of their work at professional meetings.