INTRODUCTION TO NONLINEAR DYNAMICS AND CHAOS
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Georgia Tech PHYS 4426/6268 Spring semester 2007
Predrag Cvitanovic'
Problem set 5: Baker map
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due Tue Feb 13 2007
Problem 5.0
Program baker map (5.2) in programming language of your choice
(Matlab, C, ...) and reproduce Tel and Gruiz
(a) Figure 5.1
(b) Figure 5.3
(c) Figure 5.4
(d) Figure 5.5
append a printout of your program to the problem set, or - if
you would like to have your program posted on the course homepage -
email the program to
Jonathan Halcrow gte899j [ at ] mail.gatech.edu
A java applet suitable for a lecture demonstration would
be a nice touch -:)
Problem 5.2
graduate /extra points for undergrads/
Bonus problem 27.2
Fresnel integral. Hint: use contour integration.
Motivation: Alex Silverman asks "The book mentions that to go from
a motion around a stable point to a motion around an unstable point you
can simply replace w_0 with i*s_0. Does this always work when going from
the stable solution to the unstable solution?"
Predrag: "Roughly speaking yes, but you have to be careful -
Fresnel integral is a complex rotation of the Gaussian integral, but
correct evaluation yields an extra 'geometrical' phase factor. In quantum
mechanics this factor leads to non-zero ground state energy of the
harmonic oscillator, and much important physics. So your time spent on
learning how to evaluate the Fresnel integral is a good investment."
www.cns.gatech.edu/~predrag/phys4267
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Feb 5 2007 -- Predrag.Cvitanovic@physics.gatech.edu