1. The Definition of a Dynamical System
Dynamical systems studies the long-term behaviour of evolving systems.
Here are two such systems:
In this course we will study two flavours of dynamics: topological dynamics and measure-theoretic dynamics. This course is intended to be accessible to everyone with a basic grounding in analysis, point-set topology and measure theory. Next semester in Dynamical Systems II we will study smooth dynamics and complex dynamics.
Today we covered some of the basic definitions in topological dynamics, and introduced several examples that will recur throughout the course.
The lecture notes will typically contain more material than I have time to cover in class. Anything marked with a $(\clubsuit)$ is non-examinable and you are welcome to ignore it.
It’s far too early to talk about this now, but just so you know: the Dynamical Systems I (and II) exam will be a written exam. I will only test material from the Lecture Notes and the Problem Sheets (this means that there will be no “unseen” problems.)
I encourage all students who are taking the course to join my forum (ETH/UZH login only, sorry). After joining you are asked to choose a username, and I am more than happy for you to choose something anonymous. Your email address is never shown publicly.
I will post a “Q&A” thread there after each lecture (the “Comments and Questions” button below is a direct link to today’s thread). Please do ask questions if there is anything you don’t understand, or if you spot typos in my lecture notes (and trust me, there will be LOTS of typos… ) I will try to answer every single one 😀
More information about prerequisites, recommended textbooks, the exam, and a collection of bad math jokes are also available on my forum.
Below is the PDF version of today's notes. Click on the open_in_new in the top right-hand corner to download the PDF.
Comments and questions?