CHAOS, AND WHAT TO DO ABOUT IT 
        ----------------------------------------------------------- 

	Georgia Tech PHYS 7224			 spring 2005  
	Predrag Cvitanovic'

	Lecture 4:         09:35-10:55 Thu 20 in Howey S104 

Trajectories
------------

We start out by a recapitulation of the basic notions of dynamics.
Our aim is narrow; keep the exposition focused on prerequsites to the
applications to be developed in this text.  I assume that you
are familiar with the dynamics on the level of introductory texts
such as Strogatz, and concentrate here on developing
intuition about  what a dynamical system can do.  
It will be a coarse brush sketch - 
the full description of all possible behaviors of dynamical systems is 
anyway beyond human ken.

Reading:
--------
	Classical and Quantum Chaos	---    ChaosBook.org
	chapters 2, 3

Exercises:
----------
The object is to get used to using numerical techniques to explore dynamical
systems:
	2.4) Runge-Kutta or any other integration
	2.5) Rossler system (if Poincare map too hard, postpone that part)
		then, either (easy):
	2.12) How unstable is the H\'enon attractor?
		or (will need this later anyway):
	2.13) A pinball simulator
due Thu Sept 6 at 12:25