MAST 865
Selected Topics in Dynamical Systems
Winter 2023 · Discrete Dynamical Systems, Chaos and Fractals
Topics
- Iteration of functions
- Periodic points, fixed points and bifurcations
- Sharkovsky theory
- Hénon map
- Complex dynamics
- Julia and Mandelbrot sets
- Iterated-function systems and fractals
Readings
- Saber Elaydi. Discrete Chaos, 2nd edition.
- Michael F. Barnsley. Fractals Everywhere.
Winter 2023 · Topics in Pure and Applied Mathematics
Topics
- Interpreting, analyzing, forecasting and controlling dynamic data
- Dynamic mode decomposition
- Koopman operators
- Kernel methods
- System identification
- Neural networks
- Computational scripts and notebooks for dynamical systems
Readings
- Complete instructor course notes.
- Lecture scripts and notebooks: https://github.com/jbramburger/DataDrivenDynSyst
Sources
- Course catalogue ↗2026–2027
- Syllabus or course outline ↗Winter 2023
- Syllabus or course outline ↗Winter 2023
- Winter 2023 outline. Course header explicitly lists MATH 475, MAST 661, MAST 865. Both books are explicitly recommended but not obligatory.
- Winter 2023 outline. Course header explicitly lists MATH 494, MAST 680, MAST 865. Explicitly no textbook. First-page header lists MATH 494 (MAST 680/MAST 865), whereas subsequent footers list MATH 494 (MAST 699/MAST 865); first-page header codes are preserved.