| week | date | reading | daily topics & demos | worksheets | ||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | Sep 24 Th | Intro, 1.1-1.4 | Discrete maps, fixed points, stability, cobweb plot. Periodic orbits. | cobweb, periodic | ||||||||||||||||||||||||||||||||
| 29 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 | |||||||||||||||||||||||||||||||||
| 30 W X-hr | intro53.m
| Matlab technique (by now you'll have installed it; bring your laptop) | ||||||||||||||||||||||||||||||||||
| 2 | Oct 1 Th | 1.8, 2.1 | (HW1 due) Itineraries (proof of small subintervals) | itineraries | ||||||||||||||||||||||||||||||||
| 6 Tu | 2.2-2.4 | Poincare section, 2D maps, sinks, sources, saddles, linear maps, stability (review), Jacobean. [if you need it, 4-5:30pm Intro to Matlab class, Berry Instr Ctr; sign-up reqd] | 2dlinear | |||||||||||||||||||||||||||||||||
| 7 W X-hr | - | |||||||||||||||||||||||||||||||||||
| 3 | 8 Th | 2.5 | Nonlinear maps, fixed point stability, Henon example. | |||||||||||||||||||||||||||||||||
| 13 Tu | 2.6-2.7, Challenge 2 | Stable/unstable manifolds, disc under linear map iterdisc2d.m, periodic orbits on linear map on a torus.
| manifolds | |||||||||||||||||||||||||||||||||
| 14 W X-hr | midterm review | |||||||||||||||||||||||||||||||||||
| 4 | 15 Th | 3.1-3.2 | Lyapunov exponents, chaotic orbits. | torus | ||||||||||||||||||||||||||||||||
| 20 Tu | (lecture moved to Wed X-hr) | |||||||||||||||||||||||||||||||||||
| 21 Wed X-hr | 3.3 | Binary, conjugacy, uses for logistic map | binary | |||||||||||||||||||||||||||||||||
| Midterm 1: Wed Oct 21, 6-8pm, Kemeny 007 (solutions), practise exam (solutions) On: everything up to and including 3.1, apart from Matlab. | ||||||||||||||||||||||||||||||||||||
| 5 | 22 Th | 3.4, 4.1 | Dense orbits, transition graphs and counting periodic orbits. Fractals: Cantor sets. applet, difference of two cantor sets. | transgraph | ||||||||||||||||||||||||||||||||
| 27 Tu | 4.3, 4.2 | Fractals from tent map, logistic map with a>4. Fractals from probabilistic games. Sierpinski gasket, game 1,2 | probgames | |||||||||||||||||||||||||||||||||
| 6 | 29 Th | 4.4-4.5 | (Project choice due Fri). Julia and Mandelbrot sets, Devaney movies, Fractal dimension. | mandel | ||||||||||||||||||||||||||||||||
| Nov 3 Tu | 4.6-4.7 | Fractal dimension. Box-counting dimension. Computing box-counting. Correlation dimension | boxdim | |||||||||||||||||||||||||||||||||
| 4 W X-hr | ||||||||||||||||||||||||||||||||||||
| 7 | 5 Th | 5.1-5.2, 7.1-7.2 | Lyapunov exponent for maps in Rn and their numerical measurement, lyap2d. Flows: linear (review). | |||||||||||||||||||||||||||||||||
| 10 Tu | 7.3-7.5 | Project 2-page descriptions due. Nonlinear systems of ODEs, stability. Motion in potential field. code: potential1d.m. | potential | |||||||||||||||||||||||||||||||||
| 11 W X-hr | review for midterm 2 | |||||||||||||||||||||||||||||||||||
| 8 | 12 Th | 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. | |||||||||||||||||||||||||||||||||
| 17 Tu | 8.2, 9.6 | Chaos in ODEs: Lorenz attractor. Measuring Lyapunov exponent in flows lyapflow (needs lorenz_time1map.m) | ||||||||||||||||||||||||||||||||||
| 18 W X-hr | last-minute review
| Midterm 2: Wed Nov 18, 6-8pm,
Kemeny 007 (solutions),
practise exam (solutions)
| 9 | 19 Th | Ch. 13 | Delay embedding
henon_timedelay.m.
Hamiltonian mechanics and flows: double pendulum
(applets 1, 2),
Liouville's Theorem on volume-preservation.
Autocorrelation of time-series (henon_autoc.m)
| liouville
| 24 Tu |
(no lecture)
| .................................. Nov 25 W - 29 Su Thanksgiving recess...............................
| Dec 1 Tu | Project Presentations in lecture
slot.
| 2 W X-hr | Rest of presentations
| 10 | 4 Fr | Project write-ups due (noon)
| 5 Sa - 9 W: Exam period (no final exam)
| | ||||||||||||||||||