## Week 9

 Week 9 overview Our challenge: herding cats

• 17. Markov graphs
• The topological dynamics is encoded by means of transition matrices/Markov graphs.

 Chapter 17 Walkabout: Transition graphs The chapter pdf file has hyperlinks to all videos listed below. The intention is that you study the chapter, and click on video links if you would like to see the text explained. In other words, ChaosBook is the primary mode of study, videos play only a supporting role. Let us know in a Piazza forum how this works for you. Partitions, transition matrices The bridge from determinism to statistical mechanics Symbolic dynamics Transition graphs Examples of transition graphs Tree enumeration of itineraries; pruning

• 18. Learning how to count
• Please derive yourself the trace formula the determinant and the topological zeta function. If you do not understand how to derive these, you'll be lost for the rest of the semester, and what fun is that? The lecturer seems to flounder while attempting to derive these, totally essential formulas, let him know if you have simpler derivations.

 Chapter 18 Counting Topological entropy How many walks are there? Topological trace formula Topological trace formula, take 2 Determinant of a graph Topological polynomial for complete binary dynamics Topological zeta function Loop expansion of a graph determinant Loop expansion of a graph determinant - an example Example "Loop expansion of a Markov graph" worked out step-by-step. (A paid video, recorded and edited by Stephen Murphy, GaTech PE Interactive Instructional Media) Summary
• Homework 9
•  counting  Due 15 March 2022 (note: in 1 week) Discussion forum for week 9

• Optional
•  Chaotic or not? CHAOS, a math movie with nine 13-minute chapters This is how it's done Professor Z tells me my videos do not hold candle to Physics Girl. Really? But when it comes to Socratica, I can only agree. Nice haircut. Great diction. But would you like me to tell you that "this can be said more briefly as -an isomorphism is a homomorphism and bijection"? Really? Tina Dico - Count to ten I’m gonna close my eyes; And count to ten; I’m gonna close my eyes; And when I open them again; Everything will make sense to me then

This week's videos are professionally recorded, kind courtesy of Doug Eardley, KITP, Santa Barbara CA.