week | date | reading | daily topics & demos | worksheets | ||||||||||||||||||||||||||||
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1 | Sep 22 Th | Intro, 1.1-1.4 | Discrete maps, fixed points, stability, cobweb plot. Periodic orbits. | cobweb, periodic | ||||||||||||||||||||||||||||
27 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 | |||||||||||||||||||||||||||||
28 W X-hr | intro53.m
| Matlab technique (by now you'll have installed it; bring your laptop) | ||||||||||||||||||||||||||||||
2 | 29 Th | 1.8, 2.1 | (HW1 due) Itineraries (proof of small subintervals) | itineraries | ||||||||||||||||||||||||||||
Oct 4 Tu | 2.2-2.4 | Poincare section, 2D maps, sinks, sources, saddles, linear maps, stability (review), Jacobean. | 2dlinear | |||||||||||||||||||||||||||||
5 W X-hr | ||||||||||||||||||||||||||||||||
3 | 6 Th | 2.5 | (HW2 due) Nonlinear maps, fixed point stability, Henon example. | |||||||||||||||||||||||||||||
11 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, torus | |||||||||||||||||||||||||||||
12 W X-hr | ||||||||||||||||||||||||||||||||
4 | 13 Th | 3.1-3.2 | (HW3 due) Lyapunov exponents, chaotic orbits, binary. | binary | ||||||||||||||||||||||||||||
18 Tu | 3.3, 3.4 | Conjugacy, uses for logistic map, dense orbits, transition graphs and counting periodic orbits. midterm review. | transgraph | |||||||||||||||||||||||||||||
Midterm 1: Tues Oct 18, 6-8pm, Kemeny 108 (solutions); previous exams: 2007 (solutions), 2009 (solutions). On: everything up to and including 3.1, apart from Matlab. | ||||||||||||||||||||||||||||||||
19 W X-hr | ||||||||||||||||||||||||||||||||
5 | 20 Th | 4.1 | (HW4 due Friday 5pm) Fractals: Cantor sets. applet, difference of two cantor sets. | |||||||||||||||||||||||||||||
25 Tu | 4.2, 4.3 | (Project choice due). Fractals from tent map, logistic map with a>4. Fractals from probabilistic games. Sierpinski gasket, game 1,2 | probgames | |||||||||||||||||||||||||||||
6 | 27 Th | 4.4-4.5 | (HW5 due). Julia and Mandelbrot sets, Devaney movies, Fractal dimension. | mandel | ||||||||||||||||||||||||||||
Nov 1 Tu | 4.6-4.7 | Fractal dimension. Box-counting dimension. Computing box-counting. Correlation dimension | boxdim | |||||||||||||||||||||||||||||
2 W X-hr | ||||||||||||||||||||||||||||||||
7 | 3 Th | 5.1-5.2, 7.1-7.2 | (HW6 due) Lyapunov exponent for maps in Rn and their numerical measurement, lyap2d. Flows: linear (review). | |||||||||||||||||||||||||||||
4 Fr | (Project 1-2 page description due). | |||||||||||||||||||||||||||||||
8 Tu | 7.3-7.5 | Nonlinear systems of ODEs, stability. Motion in potential field. code: potential1d.m. | potential | |||||||||||||||||||||||||||||
9 W X-hr | ||||||||||||||||||||||||||||||||
8 | 10 Th | 7.6, Ch.9, 8.1 | (HW7 due) Damping in potential field, damped pendulum. Lyapunov functions. Range of flow limit behaviors in R and R2: Poincare-Bendixson theorem. | |||||||||||||||||||||||||||||
15 Tu | 8.2, 9.6 | Chaos in ODEs: Lorenz attractor. Measuring Lyapunov exponent in flows lyapflow (needs lorenz_time1map.m) | ||||||||||||||||||||||||||||||
Midterm 2: Tues Nov 15, 6-8pm, Kemeny 108 (solutions),; previous exams: 2007 (solutions), 2009 (solutions). | ||||||||||||||||||||||||||||||||
14 W X-hr | -
9 | 15 Th |
Hamiltonian mechanics and flows: double pendulum
(applets 1, 2),
Liouville's Theorem on volume-preservation.
| liouville
| 22 Tu | Ch. 13 | Delay embedding
henon_timedelay.m.
Autocorrelation of time-series (henon_autoc.m)
Project crunch-time problem-solving session.
| .................................. Nov 23 W - 27 Su Thanksgiving recess...............................
| 29 Tu | Student project presentations in lecture
slot.
| 30 W X-hr | Rest of student presentations
| 10 | 2 Fr | Project write-ups due (noon)
| 3 Sa - 7 W: Exam period (no final exam :) )
| |