What is a topological dynamical system? The doubling map and other basics.

What is a topological dynamical system? Here we go over the basics of discrete dynamics of metrizable spaces, and we will give a handful of examples including the doubling map. Other examples come from two families of well studied cases, those of circle maps and directed graphs. After giving the definition of a topological dynamical system we go through some basic computations for these systems and then introduce the idea of topological conjugacy — the notion of equivalence we use to distinguish these systems along with an infinite family of conjugacy invariants. At the end of the video we will show that there are infinitely many non-conjugate circle maps. The video can be broken up into the following chapters: 00:00 Intro 00:25 What is a topological dynamical system? 02:10 Some examples, The doubling map and directed graphs 05:15 Basic computations for topological dynamical systems 09:58 Why is the doubling map the "doubling" map 13:40 Where do we start in mathematics? Topological Conjugacy and Invariants 17:00 Count of periodic points of a certain period is a conjugacy invariant 18:40 There are infinitely many non-conjugate circle maps. ______ Last PhD Update:    • My math research and YouTube year in revie...   Last Academic Talk/stream:    • Partial Derivative of Okamoto's Function W...   Last CHALK video:    • What is a Probability?   The CHALKboard:    / chalkboard   My website: https://nathandalaklis.com Help support my videos: https://ko-fi.com/chalknd ______ WHAT GEAR I USED FOR THIS VIDEO: Camera Kit - https://amzn.to/3PrzRKB SD card - https://amzn.to/2PbTiag Lighting Kit - https://amzn.to/3ffibMH Editing Hard Drive - https://amzn.to/2P7hSsM DISCLAIMER: Links included in this description may be affiliate links. If you purchase a product or service with the links that I include here, I may receive a small commission. There is no additional charge to you! Thank you for supporting my channel and for helping me create these free videos! =====