Dynamical systems
Undergraduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Dynamical Systems — scope drawn from open dynamical systems notes and typical US intro dynamical systems syllabi.
First-order and planar systems
- Autonomous ODEs — Autonomous ODEs
- Phase lines — Phase lines
- Bifurcations in one-dimensional systems (saddle-node, transcritical) — Bifurcations in one-dimensional systems (saddle-node, transcritical)
- Planar linear systems: classification via eigenvalues — Planar linear systems: classification via eigenvalues
- Phase plane analysis and nullclines — Phase plane analysis and nullclines
- Liapunov functions (introduction) — Liapunov functions (introduction)
Nonlinear dynamics
- Linearization — Linearization
- Hartman–Grobman theorem (statement) — Hartman–Grobman theorem (statement)
- Stable and unstable manifolds (introduction) — Stable and unstable manifolds (introduction)
- Limit cycles — Limit cycles
- Poincaré–Bendixson theorem (2D) — Poincaré–Bendixson theorem (2D)
- Hamiltonian and gradient systems (introduction) — Hamiltonian and gradient systems (introduction)
- Index theory for closed orbits (optional) — Index theory for closed orbits (optional)
Discrete dynamical systems
- Iterated maps and cobweb diagrams — Iterated maps and cobweb diagrams
- Fixed points and stability for discrete systems — Fixed points and stability for discrete systems
- Period doubling — Period doubling
- Route to chaos (logistic map) — Route to chaos (logistic map)
- Symbolic dynamics — Symbolic dynamics
- Shift maps (introduction) — Shift maps (introduction)
- Fractals and sensitive dependence (overview) — Fractals and sensitive dependence (overview)
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- First-order and planar systems
Autonomous ODEs
Coming soon - Nonlinear dynamics
Linearization
Coming soon - Discrete dynamical systems
Iterated maps and cobweb diagrams
Coming soon
Notes
Undergraduate Dynamical Systems — scope drawn from open dynamical systems notes and typical US intro dynamical systems syllabi. Topic outline: `content/topics/undergraduate/dynamical_systems.json`.