| week | date | reading | daily topics & demos | worksheets | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | Sep 17 Th | Intro, 1.1-1.4 | Discrete maps, fixed points, stability, cobweb plot. Periodic orbits. | cobweb, periodic | |||||||||||||||||||
| 22 Tu | 1.5-1.7 | Logistic family of maps, bifurcation diagram, `Periodic table' of logistic map 4x(1-x), sensitive dependence on initial conditions | table | ||||||||||||||||||||
| 23 W X-hr | intro53.m
| Matlab technique (by now you'll have installed it; bring your laptop) | |||||||||||||||||||||
| 2 | 24 Th | 1.8, 2.1 | (HW1 due) Itineraries and subinterval ordering, (proof of small subintervals) | itineraries | |||||||||||||||||||
| 26 Sa | 2.2-2.4 | Poincare section, 2D maps, sinks, sources, saddles, linear maps, stability (review), Jacobean. | 2dlinear | ||||||||||||||||||||
| 29 Tu | 2.5 |
Nonlinear maps, fixed point stability, Henon example
(henon_bifurc_anim.m).
| |||||||||||||||||||||
| 30 W X-hr | |||||||||||||||||||||||
| 3 | Oct 1 Th | 2.6-2.7, Challenge 2 |
(HW2 due)
Stable/unstable manifolds, disc under linear map iterdisc2d.m, periodic orbits on linear map on a torus.
| manifolds, torus | |||||||||||||||||||
| 6 Tu | 3.1-3.2 | Lyapunov exponents, chaotic orbits, binary. | binary | ||||||||||||||||||||
| 7 W X-hr | |||||||||||||||||||||||
| 4 | 8 Th | 3.3, 3.4 | (HW3 due) Conjugacy, uses for logistic map, dense orbits, transition graphs and counting periodic orbits. | transgraph | |||||||||||||||||||
| 13 Tu | 4.1 | Fractals: Cantor sets. applet, difference of two cantor sets. | |||||||||||||||||||||
| 14 W X-hr | midterm review | ||||||||||||||||||||||
| Midterm 1: Wed Oct 14, 6-8pm, Hald 028 (usual room). On: everything up to and including 3.1, apart from Matlab. | |||||||||||||||||||||||
| 5 | 15 Th | 4.2, 4.3 | (HW4 due Fri) Fractals from probabilistic games. Sierpinski gasket, game 1,2; IFS. Fractals from tent map, logistic map with a>4. | probgames, | |||||||||||||||||||
| 20 Tu | 4.4-4.5 | (Project choice due; discuss/email). Julia and Mandelbrot sets, Julia applet, Devaney movie. | mandel | ||||||||||||||||||||
| 21 WX-hr | |||||||||||||||||||||||
| 6 | 22 Th | 4.6-4.7 | (HW5 due). Fractal dimension. Box-counting dimension. Computing box-counting. | boxdim | |||||||||||||||||||
| 27 Tu | 5.1-5.2, 7.1-7.2 | (Project 1-2 page plan with references due). Correlation dimension. Lyapunov exponent for maps in Rn and their numerical measurement, lyap2d. Flows: linear (review). | |||||||||||||||||||||
| 28 WX-hr | |||||||||||||||||||||||
| 7 | 29 Th | 7.3-7.5 | (HW6 due). Nonlinear systems of ODEs, stability. Motion in potential field. code: potential1d.m. | potential | |||||||||||||||||||
| Nov 3 Tu | 7.6, Ch.9, 8.1 | Damping in potential field, damped pendulum. Lyapunov functions. Range of flow limit behaviors in R and R2: Poincare-Bendixson theorem. | |||||||||||||||||||||
| 4 W X-hr | review for midterm 2 | ||||||||||||||||||||||
| 8 | 5 Th | 8.2, 9.6 | (HW7 due) Chaos in ODEs: Lorenz attractor (applet). Measuring Lyapunov exponent in flows lyapflow (needs lorenz_time1map.m) | ||||||||||||||||||||
| Midterm 2: Mon Nov 9, 6-8pm, Hald 028 (usual room). On: everything since Midterm 1 up to damping in potential field. (solutions) | |||||||||||||||||||||||
| 10 Tu | Hamiltonian mechanics and flows: double pendulum (applets 1, 2), notes on Hamiltonian mechanics, equations for double pendulum. Liouville's Theorem on volume-preservation. | liouville | |||||||||||||||||||||
| 11 W X-hr | -
| 9 | 12 Th | Ch. 13 | Integrable/chaotic Hamiltonian systems.
Time-delay embedding, timedelaydemo,
needs the four time-series made by make_timeseries.
| 17 Tu | Student project presentations in lecture
slot.
| 18 W X-hr | Remaining student presentations
| 23 M | 9am. Project write-ups due.
| 20 Fr - 25 W: Exam period (we have no final exam :) )
| | |||||||||||