Topics in Dynamical Systems - Fixed Points, Linearization, Invariant Manifolds, Bifurcations & Chaos

This course gives a high-level introduction to dynamical systems, including fixed points, linearization, eigenvalues and eigenvectors, invariant manifolds, bifurcations, discrete-time dynamics, trajectory integration, and chaos. Examples include the Duffing oscillator, population dynamics, fluid mixing, and the Lorenz system.

Syllabus

Introduction
Linearization at a Fixed Point
Why We Linearize: Eigenvalues and Eigenvectors
Nonlinear Example: The Duffing Equation
Stable and Unstable Manifolds
Bifurcations
Discrete-Time Dynamics: Population Dynamics
Integrating Dynamical System Trajectories
Chaos and Mixing