Amir Sagiv II: Mini-course on Dynamical Systems
Speaker: Amir Sagiv (Part II)
Date: 07-08-21 10:30AM EST
Link: Lecture
Syllabus/Attachments: DynSys21.pdf / Exercises.pdf
Notes: Notes.pdf
Abstract: INTRODUCTION TO DYNAMICAL SYSTEMS (mini-course)
Dynamical systems are a ubiquitous element of modeling. At the center of this field is a simple fundamental question - how do local, first-principle forces, shape the overall trajectory of a system in time? In this mini-course, we will focus on ordinary differential equations (ODEs), where the state of the system is prescribed by a vector in R^d or C^d. The starting point will be the following inconvenient fact: given an ODE
x’(t)=f(x,t), x(t_0)=x_0
we can rarely obtain explicit closed-form solutions. What information on the solutions can we still extract from such models? We will briefly touch on the following topics:
• Phase space portraits and long time asymptotics • Fixed points, stability and instability, limiting cycles • Bifurcations • Discrete systems and chaos • Numerical methods and numerical study of dynamical systems