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| 1 | Sep 26 W | Intro, 1.1-1.3 | Discrete maps, fixed points, stability, cobweb plot. | cobweb | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 27 Th X-hr | intro53.m
| Crash course in Matlab (useful to install it & bring your laptop) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 28 F | 1.4-1.5 | Periodic orbits, logistic family of maps, bifurcation diagram | periodic | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Oct 1 M | 1.6-1.7 | `Periodic table' of logistic map 4x(1-x), sensitive dependence on initial conditions | table | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| 2 | 3 W | this | discussion/demos w/ sound artist Stephan Moore of Merce Cunningham dance residency on chance and chaos in the arts
| 4 Th X-hr | (free) [suggest 4-6pm Intro to Matlab class, Berry Instr Ctr; sign-up reqd]
| 5 F | 1.8 | (HW1 due) Itineraries | itineraries
| 8 M | 2.1-2.2 | Poincare section, 2D maps, sinks, sources, saddles
| 3 | 10 W | 2.3-2.4 | Linear maps, stability (review), Jacobean
| 2dlinear
| 11 Th X-hr |
| 12 F | 2.5 | Nonlinear maps, fixed point stability, Henon example.
| 15 M | 2.6-2.7 | Stable/unstable manifolds, disc under linear map | iterdisc2d.m
manifolds
| 4 | 17 W | Challenge 2, 3.1 | Periodic orbits on linear map on a torus,
Lyapunov exponents. [suggest 4-6pm Programming in Matlab
class, Berry Instr Ctr; sign-up reqd].
| torus
| 18 Th X-hr |
| 19 F | 3.1-3.2 | Lyapunov exponents, Chaotic orbits.
| 22 M | 3.3 | Binary, conjugacy, uses for logistic map | binary
| Midterm 1: Tues Oct 23, 6-8pm, Silsby 028 (on everything
apart from Matlab - note evening + weird location)
| 5 | 24 W | 3.4 | Dense orbits, transition graphs and counting periodic orbits | transgraph
| 25 Th X-hr |
| 26 F | 4.1, 4.3 | Fractals: Cantor sets, fractals from tent map,
logistic map with a>4. applet, difference of two cantor sets.
| 29 M | 4.2 | fractals from probabilistic games.
Sierpinski
gasket, game 1,2 | probgames
| 6 | 31 W | 4.4 | Project choice due. Julia and Mandelbrot sets
Devaney movies
| Nov 2 F | 4.5 | Fractal dimension. Box-counting dimension.
| 5 M | 4.6-4.7 | Computing box-counting. Correlation dimension | boxdim
| 7 | 7 W | (lecture postponed to Thurs X-hr)
| 8 Th X-hr | 7.3-7.4 | Flows: linear (review) and nonlinear
systems of ODEs, stability.
| 9 Fr | 7.5 | Motion in potential field. code: potential1d.m
| 12 M | 7.5-7.6 | More motion in potential field, damping,
damped pendulum
| potential
| 8 | 14 W | 7.6, Ch.9 | Project 2-page descriptions due.
Lyapunov functions.
| 15 Th X-hr | Review session
| Midterm 2: Thurs Nov 15, 6-8pm, Silsby 028 (note evening + weird location)
| 16 Fr | 8.1, 8.2 | Range of flow limit behaviors in
R and R2: Poincare-Bendixson theorem.
Chaos in ODEs: Lorenz attractor.
| 19 M | 5.1, 5.2, 9.6 | Lyapunov exponent
for maps in Rn and flows: numerical measurement,
lyap2d,
lyapflow (needs
lorenz_time1map.m)
| .................................. Nov 21 W - 25 Su Thanksgiving recess
............................... | 9 | 26 M | Ch. 13 | Delay embedding
henon_timedelay.m.
| 28 W | Hamiltonian mechanics and flows: double pendulum
(applets 1, 2),
billiards
| 29 Th X-hr | Liouville's Theorem on volume-preservation.
Autocorrelation of time-series (henon_autoc.m)
| liouville
| 30 F | (no lecture - Alex out of town)
| 10 | Dec 3 M | Project Presentations in lecture,
continue in evening (6-8pm) with pizza.
| 5 W | (no lecture)
| 6 Th | Project write-ups due (noon).
| 7 Fr - 11 Tu: Exam period (no final exam)
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