CHAOS, AND WHAT TO DO ABOUT IT ----------------------------------------------------------- Georgia Tech PHYS 7224 spring 2005 Predrag Cvitanovic' Lecture 17: 9:35-10:55 Thu ??? 16 in Howey S106 Cycle expansions -- Homework Assignment #12 ---------------- Reading: -------- chapter 15 - Cycle expansions Project: -------- complete the part planned for ??? 23, write up a current status (I recommend you write results into a continuously updated LaTeX file, it is a necessary skill if you plan to do research in physics or math). If you failed to attain the goal for ??? 23, explain why. Dog ate the project is an accepted answer if accompanied by the report by a certified forensic canine crime specialist. For an example of an outline, see Tyson's project on the project homepage. Exercises: (both are optional) ---------- 12.1: Escape rate for a 1-d repeller, numerically (you have already done it in assignment #10 - but you might want to tweak it up, in order to get a more precise estimate to compare the number with the cycle expansion result, next exercise) 15.2 Escape rate for a 1-d repeller, periodic orbit theory (the tricks for finding cycles are descibed in chapter 14, and in the next lecture: good to work through this all the way - you might also find reading the solution ChaosBook.org/chapters/solutions.ps.gz helpful in uderstanding the material) due Thu ??? 23 2005