Symbolic Dynamics - Chaos Theory | Lecture 4

Abstraction is the language of mathematics. In this lecture we learn about the abstract space of infinite binary sequences. We show that this space can be endowed with a metric (a distance measure) and we can define a continuous function on the space called the shift map. The shift map turns out to be a chaotic function (shown in coming lectures) whose dynamics are incredibly simple to understand. All of this abstract work in this lecture will culminate in the next one where we use symbolic dynamics and the shift map to classify and understand the dynamics of the fractal invariant set we found in the logistic map in the previous lecture. More information on the instructor: https://hybrid.concordia.ca/jbrambur/ Follow @jbramburger7 on Twitter for updates. Image attributions for the thumbnail: 1. “Binary Flow”, by Dawn Hudson, licensed under CC0 Public Domain. Source: PublicDomainPictures.net, image ID 148316. publicdomainpictures.net 2. “Binary Numbers”, photograph by Mandeep Singh, uploaded 26 September 2020. Licensed under CC0 – Free to Use, Attribution Optional. Source: PixaHive.