Mathematical Sciences: Undergraduate Research in Analysis and Dynamical System

数学科学：分析与动力系统本科研究

• 批准号: 9100590
• 负责人: David Carothers
• 金额: $ 0.7万
• 依托单位: Hope College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-03-01 至 1992-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9100590&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Undergraduate; Research; Analysis

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.

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组合以及通过组成这些组合的凸组合而得到的结构。这项工作扩展了早期的研究，结合了在马尔可夫算子研究中发生的测度保持变换。对动力系统的研究将集中在最近发展起来的伪轨道遮蔽思想上。阴影测量的是一个轨道能被附近轨道追踪到的程度。这种现象很重要，因为具有阴影特性的动力系统可以在计算机上建模。学生将被鼓励在专业会议上展示他们的工作成果。