LECTURE NOTES

Scanned and powerpoint lecture notes.

WARNING: downloading the lecture notes and putting them under your pillow at night will not help you learn the material.
Same for putting the textbook under your pillow. I tried it for many years without success.

If you would like to have the movies that I showed, please come to see me to copy them directly from my computer - most of them are very large.

Lecture 1: A global overview of nonlinear dynamics and chaos
Lecture 2: Flows on the line
Lecture 3: Bifurcations (part 1). Saddle-nodes and transcritical bifurcations. Normal forms.
Lecture 4: Bifurcations (part 2). Pitchforks. Example of the bead on a hoop. Imperfect bifurcations. Notion of co-dimension.
  Lecture 5 and 6: Applications of 1D continuous systems: Population dynamics
Lecture 6 and 7: Introduction to 2D systems. Linearization around fixed points.
Lecture 8: Solutions of linear systems and classification of fixed points.
Lecture 9: Example of a 2D dynamical system: the pendulum. Effects of nonlinear terms on the linear stability of fixed points.
Lecture 10: General discussion of structural stability. Example of the predator-prey model. Conservative and reversible systems.
Lecture 11: Limit cycles.
Lecture 12: The solar dynamo. An example of 3D continuous systems, and an introduction to bifurcations.
Lecture 13: Introduction to discrete systems. 1D Maps.
Lecture 14: The Logistic Map in detail. Universality and Period Doubling route to Chaos.
Lecture 15: Definition of Chaos. Lyapunov exponents; examples. The Tent Map
Lecture 16: From dynamical systems to Fractals. The Tent Map in detail. Definition of Fractals.
Lecture 17: 2D maps
Lecture 18: Fundamental examples of dynamical systems: 1. the restricted  3-body problem
Lecture 19:  2. The Lorenz equations