Introduction to
Nonlinear Dynamics and Chaos

svn: $Author: predrag $ - $Date: 2007-06-11 09:54:53 -0400 (Mon, 11 Jun 2007) $

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

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)

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)

grades deadline Mon, May 7

Predrag Cvitanović