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Introduction to
Nonlinear Dynamics and Chaos
svn: $Author: predrag $ - $Date: 2007-06-11 09:54:53 -0400 (Mon, 11 Jun 2007) $
Course Schedule
Part I: Complex motion, unusual geometry
- January 9
1. A brief history of motion in time
-
The introductory lecture (as well as many to follow) will complement the
material covered in the textbook.
Reading: Chapter 1
Optional reading:
overheads (first lecture pictures)
ChaosBook.org Brief history
of chaos
might amuse you.
- January 11
2.
Fractal objects
-
Lecture will complement the material covered in the textbook.
Reading: all of Chapter 2 except sections 2.2.2, 2.2.3
Problem set 1:
2.1, 2.8, 2.15,
2.16
(solutions)
- January 15
Institute holiday - MLK Day
Part II: Introductory concepts
- January 16
3. Regular motion
- Reading: Chapter 3,
sections
3.1, 3.2
- January 18
4. Regular motion
- Reading: Chapter 3,
sections
3.3, 3.4, 3.5
Problem set 2:
3.1, 3.2,
3.7,
3.15,
3.22,
3.4,
3.8
(solutions)
- January 23
5. Regular motion
- Reading:
Chapter 3, section 3.5.2
- January 25
6. Driven motion
- Reading:
Chapter 4, sections 4.1, 4.2;
Appendix A.1.1
Problem set 3:
3.24,
4.2,
4.3,
3.23
(solutions)
- January 30
7. Driven motion
- Reading:
Chapter 4, section 4.3;
Appendix A.1.2
- February 1
8. 2- and 3-d flows and maps summarized
- Reading: Chapter 4, sections 4.4 - 4.8
Optional reading:
analytic example (not in the book)
Problem set 4:
4.5, 4.8, 4.9, 4.11,
4.7
(solutions)
Part III: Investigation of chaotic motion
- February 6
9. Chaos in dissipative systems
- Reading: Chapter 5, sections 5.1, 5.2
Optional reading:
Game of pinball (grateful for any suggestions
how to improve this, edits, ...)
- February 8
- guest lecture by
Rytis Paškauskas
10. Baker map
- Reading: Chapter 5, sections 5.3-5.2.2
Problem set 5
-
(solutions)
bonus problem 27.2
-
(solution)
- February 13
11. Homoclinic tangle
- Reading: any other book, for example Ott or
scholarpedia.org (if you find something good, let me know)
- February 15
12. Lozi map
- Reading: Chapter 5,
5.2.4 - 5.2.6 (skip section 5.2.3)
Problem set 6
-
(solutions, preliminary)
- February 20
13. Universality in chaos
- Reading: Chapter 5, section 5.3
- February 22
14. Midterm
exam
-
reading list
-- problem 1
-- problems 2,3 and solutions
No problem set this week.
- February 27
- NOTE: 9:15am undergrads meeting
15. Universality in chaos
- Reading: Chapter 5, section 5.3;
Universality in transitions to
chaos
[2p. per page version]
(grateful for any suggestions
how to improve this, edits, ...)
- March 1
16. From 3d flows
to 1d maps
- Reading:
Rossler system
Problem set 7: exercises
1, 2, 4,
3;
bonus points for all:
exercise 5. Compute stability eigenvalues of the two equilibria.
exercise 7. Intrinsically parametrized Rossler map (a good solution set
goes straight into ChaosBook.org)
Do not copy Rytis - do your own, it will be simpler.
- March 6
17. Return maps, period doubling
- March 8
18. Measures of chaos
- Reading: Section 5.4, skip 5.4.3, 5.4.6
Problem set 8,
exercise 26.1
-
(solutions)
- March 13
19. Natural measures
- Reading: Section 5.5
- March 15
20. Measures of chaos
- Reading: Chapter 5, p. 186, box 5.6; skip sections 5.6, 5.7
Reading:
Transporting densities, sections 9.1, 9.2, 9.3
Problem set 9:
5.35,
5.34;
bonus-points problem for everybody:
exercise 9.5
(solutions ,
solution to 9.5)
- March 19-23
Midterm recess
- March 27
21. Transient chaos
- Reading: Chapter 6, section 6.1, 6.2, 6.3; skip fractal dimensions
parts, as well as section 6.3.3
- March 29
22. Horseshoes
- Reading: Chapter 6, sections 6.4, 6.5
Problem set 10:
6.1, 6.2,
6.10
(solutions)
- April 3
23. Putting order into chaos
- Reading: Qualitative dynamics, for pedestrians,
sections 11.3, 11.4
Optional reading: How Dame Mary L. Cartwright discovered chaos in 1940's.
- April 5
24. Conservative chaos
-
Reading: Chapter 7, sections 7.1, 7.2
Problem set 11:
11.1, 11.6,
11.7;
bonus-points problem for everybody:
12.1
(solutions,
solution to 11.7)
- April 10
25. Combinatorics, prime cycles
-
Reading: Chapter 7, section 7.3
- April 12
26. Standard map, diffusion, KAM
-
Reading: Chapter 7 - read section 7.4, but skip the algebra;
sections 7.5, 7.6, 7.7
Problem set 12:
11.7 (well executed parts (b) and (f)
might earn bunch of bonus points
and your immortalization in ChaosBook.org);
7.2, 7.4,
7.8;
bonus-points problem for everybody:
7.9
how to contribute figures to ChaosBook.org
(solutions)
- April 17
27. Chaotic scattering
- Reading: Chapter 8, sections 8.1, 8.2, skip the rest
Optional reading: high school geometry version
- April 19
28. Turbulence
- April 24
29. Nonlinear locomotion, nonlinear heart
- No reading: decerebrated frogs, giant squids and
dog hearts
-
take-home final exam
- Reading: Turbulence?
Demo of Kuramoto-Sivashinsky simulations, by
Ruslan L. Davidchack
- April 26
30. Brain: do not leave home without it
- No reading, freebie lecture:
- "Decoding Neural Signals for the Control of Movement", by
Solla, Rebesco, Miller and Hatsopoulos
- Friday Apr 27
classes end
-
take-home final exam
due no later than
10:50am Thu, May 3
delivered either to Jonathan or Predrag, 5th floor Howey
(solution by Matt Marshall)
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grades deadline Mon, May 7
Predrag Cvitanović