M10 · Nonlinear dynamics & chaos
A 26-module path through m10 · nonlinear dynamics & chaos, in study order from foundations to the frontier.
Modules
- Phase Portraits and the Phase Plane
- Fixed Points and Equilibria
- Linear Stability Analysis and the Jacobian
- Classification of Fixed Points: Nodes, Saddles, Spirals, Centers
- Conservative Systems and Hamiltonian Phase Flow
- Limit Cycles and Self-Sustained Oscillations
- The Van der Pol Oscillator
- Poincaré–Bendixson Theorem
- Bifurcations and the Loss of Stability
- Saddle-Node, Transcritical, and Pitchfork Bifurcations
- Hopf Bifurcation and Birth of Limit Cycles
- Period-Doubling Cascade and the Route to Chaos
- Feigenbaum Constants and Universality
- The Driven Damped Pendulum
- The Double Pendulum
- Sensitive Dependence on Initial Conditions
- Lyapunov Exponents
- Strange Attractors and Fractal Dimension
- Poincaré Sections and Return Maps
- Discrete Maps and the Logistic Map
- Integrable Systems and Action-Angle Variables
- The KAM Theorem
- Resonant Tori, Resonance Overlap, and the Chirikov Criterion
- The Standard Map and Chaotic Hamiltonian Dynamics
- Homoclinic and Heteroclinic Orbits and the Smale Horseshoe
- The Lorenz System