Mathematical Sciences: Undergraduate Research in Analysis and Dynamical System

该奖项支持两名本科生在 主要研究者对研究中的问题的指导 数学分析与动力系统 的工作 分析集中在与类相关的几何问题上， 连续函数 具体来说，学生会考虑 连续函数的合成与结构 通过形成组合物的凸形组合而获得。 的 工作扩展了早期的调查与措施的组合 保持马尔可夫研究中出现的变换 运营商 对动力系统的研究最近将集中在 提出了伪轨道跟踪的概念。 跟踪措施 一个轨道可以被附近轨道跟踪的程度。 的 现象是重要的，因为动力系统与 阴影特性可以在计算机上建模。 学生将被鼓励提出他们的结果 参加专业会议。

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.