CHAOS, AND WHAT TO DO ABOUT IT / homework teams
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	Georgia Tech PHYS 7224			spring 2005  

						Homework Assignment #3
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						due Tue, Feb 8

Exercises (two weeks worth):
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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
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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 
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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.