INTRODUCTION TO
NONLINEAR DYNAMICS AND CHAOS
  

Next lecture

TEXT:  Steven H. Strogatz: Nonlinear Dynamics and Chaos (Addison-Wesley 1994). All chapter and exercise numbers refer to this book, unless stated otherwise.
Some material and problem sets from Classical and Quantum Chaos webbook, available on www.nbi.dk/ChaosBook/

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Lecture 1          2:30 - 4:00 tuesday, March 30, 1999 in Tech M120
Preview; Basic properties of differential equations
A brief historical introduction to the subject.
Reading: chapter 1; chapter 2, sections 2.1-2.3
Optional reading: Historical appendix of the webbook might be amusing reading.
Problems: 2.1.1, 2.1.2, 2.1.3, 2.2.7, 2.2.11

Lecture 2          2:30 - 4:00 thursday, April 1, 1999 in Tech M120
One-dimensional dynamics; Bifurcations
Reading: chapter 2, chapter 3, sections 3.0-3.3
Optional reading: Sect 4.1 of the webbook, for a more abstract definition of dynamical systems.
Problems: 2.4.7, 2.6.1, 2.7.3, 2.8.6

Lecture 3          2:30 - 4:00 tuesday, April 6, 1999 in Tech M120
Bifurcations
Reading: all of chapter 3
Problems: 3.1.2, 3.1.3, 3.2.2, 3.4.4, 3.5.4, 3.6.5

Lecture 4          2:30 - 4:00 thursday, April 8, 1999 in Tech M120
Bifurcations
Reading: chapter 3

Lecture 5          2:30 - 4:00 tuesday, April 13, 1999 in Tech M120
Flows on the circle
Reading: chapter 4, sections 4.0-4.4
Problems: 4.1.2, 4.3.1, 4.3.2

Lecture 6          2:30 - 4:00 thursday, April 15, 1999 in Tech M120
Two-dimensional systems
Reading: Chapter 5
Problems: 5.1.1, 5.1.9, 5.2.1, 5.2.6, 5.2.13

Lecture 7          2:30 - 4:00 tuesday, April 20, 1999 in Tech M120
Conservative systems and index theory
Reading: chapter 6
Problems: 6.1.2, 6.1.10, 6.3.2, 6.3.10, 6.5.8-10, 6.5.19

Lecture 8          2:30 - 4:00 thursday, April 22, 1999 in Tech M120
Conservative systems and index theory
Reading: chapter 7
Problems: 7.1.9, 7.2.9

Lecture 9          2:30 - 4:00 tuesday, April 27, 1999 in Tech M120
Poincaré-Bendixson theorem
Reading: chapter 7
Problems: 7.3.1

Lecture 10         2:30 - 4:00 thursday, April 29, 1999 in Tech M120
Non-linear oscillators and averaging
Reading: chapter 7
Problems: 7.5.3, 7.6.13

Lecture 11         2:30 - 4:00 tuesday, May 4, 1999 in Tech M120
Bifurcations in two-dimensional systems
Reading: chapter 8
Problems: 8.1.4, 8.1.11, 8.2.1, 8.2.5

Lecture 12         2:30 - 4:00 thursday, May 6, 1999 in Tech M120
Bifurcations in two-dimensional systems
Reading: chapter 8
Optional reading (not required in the course): the damped driven pendulum, Tomas Bohr's notes.
Problems: 8.3.1, 8.7.3

Lecture 13         2:30 - 4:00 tuesday, May 11, 1999 in Tech M120
Lorenz equations
Reading: chapter 9, sections 9.0, 9.2
Why Dame Mary L. Cartwright discovered chaos in 1940's.
Problems: 9.2.2, 9.2.4, 9.2.6, 9.4.2 (J.M.: 9.1.4, 9.2.2)

Lecture 14         2:30 - 4:00 thursday, May 13, 1999 in Tech M120
Lorenz system, one-dimensional maps
Reading: chapter 9, sections 9.3-9.5; chapter 10, sections 10.0-10.4
Optional reading: Sect 4.2 of the webbook, stability/Jacobinas of flows.
Problems: 9.2.4, 9.3.9, 9.4.2, 10.1.9
Projects: the current term projects are listed on www.nbi.dk/ChaosBook/projects/; please get in touch with me soon if you have a project proposal.
Final exam: current plan is to give you a small project-length problem Friday morning June 4. The problem would involve analysis of a dynamical system (fixed points, stability, bifurcations) and numerical experimentation with integration of a set of differential equations describing the system. Due date would be 2:30 PM June 8, 1999, my office.

Lecture 15         2:30 - 4:00 tuesday, May 18, 1999 in Tech M120
One-dimensional maps
Reading: chapter 10, sections 10.5-10.7
Problems: 10.1.12, 10.1.13, 10.2.6, 10.4.5

Lecture 16         2:30 - 4:00 thursday, May 20, 1999 in Tech M120
Renormalization theory; fractals
Reading: chapter 10, sections 10.6-10.7; chapter 11
Problems: 10.7.4, 11.3.3, 11.4.6

Lecture 17         2:30 - 4:00 tuesday, May 25, 1999 in Tech M120
Strange attractors
Reading: chapter 12

Lecture 18         2:30 - 4:00 thursday, May 27, 1999 in Tech M120
Chaotic averaging: escape rates

Reading period starts

Lecture 19         2:30 - 4:00 tuesday, June 1, 1999 in Tech M120
Chaotic averaging: escape rates?
Problems: we concentrate on the term paper projects

Lecture 20 (the last of the course)     2:30 - 4:00 thursday, June 3, 1999 in Tech M120
What's wrong with this course?
A moment of truth; exhaustion has sat in, so we cancelled the lecture.

Alernative:
Term papers