NONLINEAR DYNAMICS: QUANTUM CHAOS  
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	Georgia Tech PHYS 7224			Spring semester 2002  
	Predrag Cvitanovic'

	Lecture 22         Tue, Apr 2 2002 12:05-13:25 in Howey S106


Discrete symmetries 
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Dynamics often comes equipped with discrete symmetries, 
such as the reflection and the rotation symmetries.
Symmetries simplify and improve the cycle expansions in a
rather beautiful way. 


Reading:
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	Classical and Quantum Chaos	
        ---    www.nbi.dk/ChaosBook/postscript.html

chapter 17 - Discrete symmetries 
	
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The solution of problems starting with helium trajectories and ending with
the helium spectrum form the final exam in the course. 

If you prefer, 
you can compute the 3-disk resonances instead, the determination
of perioidc orbits is easier in billards than it is in the flows.
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