Week 9
Week 9 overview  
Our challenge: herding cats 
 17. Markov graphs / 6 March 2018 /
 18. Learning how to count / 8 March 2018 /
 Homework 9
 Optional
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 
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 stepbystep. (A paid video, recorded and edited by Stephen Murphy, GaTech PE Interactive Instructional Media) 

Summary 
counting Due 20 March 2018 

Discussion forum for week 9 
Chaotic or not? CHAOS, a math movie with nine 13minute 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.