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CHAOS, AND WHAT TO DO ABOUT IT

JClub06 PHYS 7224  -  fall 2007
Tu,Th 1:35-2:55 Howey S204

ChaosBook.org/~predrag/courses/PHYS-7224-07
svn: $Author: predrag $ - $Date: 2007-12-14 17:50:50 -0500 (Fri, 14 Dec 2007) $
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Course Schedule

Always download chapters from this homepage, rather than from ChaosBook.org . This homepage is more up-to-date.

August 21
1. A brief history of motion in time
brief description
Chapter 1 - Overture [solutions to exercises]
Appendix A. Brief history of chaos (optional reading)
lecture overheads
homework #1: (1.1) and (1.2) due Tue Aug 28,


part I: Geometry of chaos

August 23
2. Trajectories
brief description
Chapter 2 - Flows [solutions to exercises]
homework #2: (2.1), (2.7), and (2.8), optional (2.6) due Tue Sep 4.
August 28
3. Maps
brief description of exercises
Chapter 3 - Do it again [no solutions available as yet]
homework #3: (3.1) and (3.2), due Tue Sep 4.
August 30
4. Stability
Chapter 4 - Local stability [solutions to exercises]
homework #4: (4.1), (4.3) and (4.4), due Tue Sep 11.
September 3
Labor Day
September 4
5. Cycle stabilities are invariant
Chapter 5 - Cycle stability [solutions to exercises]
Chapter 6 - Get straight (optional reading) [solutions to exercises]
Chapter 7 - Newtonian dynamics (optional reading)
September 6
6. Billiards
Chapter 8 - Billiards [solutions to exercises]
September 11
7. Billiard dynamics, stabilities
Chapter 9 - World in a mirror (optional reading) [solutions to exercises]
homework #5: (7.1), (7.2), (7.3), extra points: (7.4), (7.6) - due Tue Sep 18.
September 13
8. Partitioning state space
Chapter 10 - Qualitative dynamics, for pedestrians [solutions to exercises]
September 18
9. Kneading theory
homework #6: (8.3), (7.5), (10.4), (10.6) extra points: (8.4), (10.5) - due Thursday Sep 27.
September 20
10. Markov graphs
Chapter 11 - Qualitative dynamics, for cyclists [solutions to exercises]
September 25
11. Stretch and fold for pro bakers
homework #7: (11.1), (11.3) extra points: (11.7), (11.9) - due Tue Oct 2
September 27
12. Fixed points: where are they?
Chapter 12 - Fixed points, and how to get them [solutions to exercises]


part II: Chaos rules

October 2
13. Chaos for accountants
Chapter 13 - Learning how to count [solutions to exercises]
homework #8: (12.1), (12.3); either (12.5) pinball or (12.7) Rossler; optional (12.2), (12.6), (12.10) - due Tue Oct 16
October 4
14. Topological entropy
our first trace formula, the rest is details
October 6-9
Midterm recess
October 11
15. Topological zeta function
determinants of graphs; fear not infinite partitions

Friday Oct 12    last day to drop the course

October 16 - lecturer John F. Gibson
16. Learning how to measure
Chapter 14 - Transporting densities [solutions to exercises]
homework #9: 9.5 (from the current version Chap 9); 13.3, 13.4, 14.1, 14.3, 14.5 ; optional 13.15, 14.7 - due Thu Oct 25
October 18 - lecturer John F. Gibson
17. Not your average theory
Chapter 15 - Averaging [solutions to exercises]
October 23 - lecturer John F. Gibson
18. All that was left was a trace
Chapter 16 - Trace formulas [solutions to exercises]
homework #10: 14.10 (from the current version Chap 14), 15.2, 15.4, 17.2 - due Tue Oct 30
October 25 - lecturer John F. Gibson
19. And trace again
October 30 - lecturer Alexander Grigo
20. Determined we push on
Chapter 17 - Spectral determinants [no solutions available as yet]
homework #11: 17.5, 17.11, 18.1, 18.2 optional: 17.10, 18.4 - due Tue Nov 6 (no solutions available as yet)

Wednesday, Oct 31    spring registration starts; may we recommend the Group Theory course?

November 1 - lecturer John F. Gibson
21. Recycle: it's the law
Chapter 18 - Cycle expansions [no solutions available as yet]
November 6 - lecturer John F. Gibson
22. Recycling recycling
homework #12: 9.7, optional: 9.6, 9.8 - due Tue Nov 13
November 8 - lecturer John F. Gibson
23. Still recycling

Tuesday, Nov 13    spring registration ends

November 13
24. Cycling for (discrete) fundamentalists
Chapter 9 - World in a mirror (optional reading) [solutions to exercises]
homework #13: 18.7, 18.8, 19.3, optional 19.5 - due Tue Nov 20
November 15
25. Cycling for (smooth) fundamentalists
Chapter 19 - Symmetry factorization [no solutions available as yet]
November 20
26. Still discretely back pedaling
no homework this week

November 22-25
Institute holiday - Thanksgiving
November 27
27. Symmetry factorization of spectral determinants
homework #14: 23.1, 23.2, 23.3, optional 23.6 - due Tue Dec 4


part III: Chaos is your friend

projects: template, open
November 29
28. From deterministic chaos to nonequilibrium statistical mechanics
Chapter 20 - Why cycle? (optional reading) [solutions to exercises]
Chapter 21 - Why does it work? (optional reading) [solutions to exercises]
Chapter 23 - Deterministic diffusion [solutions to exercises]
December 4
29. Sometimes They come back
Chapter 22 - Intermittency (optional reading) [solutions to exercises]
December 6
30. All the group theory you will ever need in one easy lectures
Chapter 137 - Lie groups for cyclists (regrettably still unwritten)

Friday Dec 7:    classes end

Friday December 14
10:55am Chaos project due

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grades deadline            Mon Dec 17

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svn: $Author: predrag $ - $Date: 2007-12-14 17:50:50 -0500 (Fri, 14 Dec 2007) $