Mini-course: Understanding nonlinear dynamics with finite data (Lecture 2)

Abstract

This set of tutorial lectures will focus on five topics:

1. I will provide an extremely a brief description of the subject of dynamical systems and argue that as currently framed is too rich a subject in an area of data driven science and engineering.  
2. I will describe a courser approach to dynamics that is based on combinatorics, order theory, and algebraic topology.  
3. I will discuss computational aspects and challenges associated with this new approach.
4. I will describe how some results from classical dynamics can obtain via this approach.
5. I will present some applications.