Nonlinear Dynamics: Chaos

Lecture Notes

Lecture 1: Introduction to Nonlinear Dynamics: Chaos (PDF)

Lectures 2–3: Flows and Bifurcations in One Dimension (PDF)

Lectures 4–5: Pendulum and Stability in Two Dimensional Systems (PDF)

Lectures 6–7: Dissipation and Contraction of Volumes in Phase Space (PDF)

Lectures 8–9: Forced Oscillators and Limit Cycles (PDF)

Lectures 10–11: Bifurcations in Two Dimensions (PDF)

Lectures 12–14: Spectral Analysis for Dynamical Systems (PDF)

Lectures 15–16: Poincaré Sections (PDF)

Lectures 17–18: Fluid Dynamics and Rayleigh-Benard Convection (PDF)

Lecture 19: Introduction to Strange Attractors (PDF)

Lectures 20–21: Lorenz Equations (PDF)

Lecture 22: Hénon Attractor (PDF)

Lecture 23: Fractal Dimension (PDF)

Lecture 24: Lyapunov Exponents (PDF)

Lectures 25–27: Period Doubling Route to Chaos (PDF)

Lecture 28: Intermittency (and Quasiperiodicity) (PDF)