CHAOS, AND WHAT TO DO ABOUT IT / homework teams --------------------------------------- Georgia Tech PHYS 7224 spring 2005 Homework Assignment #3 ---------------------- due Tue, Feb 8 Exercises (two weeks worth): ---------- Without numerical simulations there is no exploration of dynamics: 2.6 program Runge-Kutta (or any other integrator) 2.7 integrate numerically Rossler system using your integrator 3.1 construct a Poincare section for the Rossler system Analytic exercises: 4.1 (you will use this in many theory courses) 3.4 Henon fixed points 2.8 equilibria of Rossler 4.3 topology of Rossler flow Bonus points: 2.9 Integrate this? 3.5 How strange is the H\'enon attractor? 3.6 Fixed points of maps 4.2 Stability, diagonal case 5.2 When is a linear transformation canonical? www.cns.gatech.edu/~predrag/courses/PHYS-7224-05/duedates.html ChaosBook.org/version11/chapters/exerFlows-2p.ps.gz ChaosBook.org/version11/chapters/exerMaps-2p.ps.gz ChaosBook.org/version11/chapters/exerStability-2p.ps.gz Homework teams -------------- Please self-organize into homework teams of two or three students each in order to share the coding/debugging for numerical exercises (here 2.6, 2.7 and 3), and let me know who is on which team, and which programming languages you know: www.cns.gatech.edu/~predrag/courses/PHYS-7224-05/homeworkTeams Slaven Peles' Re. exer 3.1 -------------------------- An example of a Poincare section is the code which calculates stroboscopic map for a driven pendulum, ChaosBook.org/extras/Peles/pendulum.c Perhaps you can modify to calculate Poincare map for the Rossler system. You need GNU Scientific Library (GSL) package installed on your computer to compile the code. It is installed on a several machines in physics graduate student computer lab (Howey building, ground floor). Check http://www.cns.gatech.edu/~predrag/courses/PHYS-7224-05/info.html for more on GSL and Quantian.