# Math 53, FALL 2011: Schedule, topics and worksheets

week   date    readingdaily topics & demosworksheets
1Sep 22 Th Intro, 1.1-1.4 Discrete maps, fixed points, stability, cobweb plot. Periodic orbits. cobweb, periodic
27 Tu1.5-1.7Logistic family of maps, bifurcation diagram, `Periodic table' of logistic map 4x(1-x), sensitive dependence on initial conditionstable
28 W X-hr`intro53.m` Matlab technique (by now you'll have installed it; bring your laptop)
229 Th1.8, 2.1(HW1 due) Itineraries (proof of small subintervals) itineraries
Oct 4 Tu2.2-2.4Poincare section, 2D maps, sinks, sources, saddles, linear maps, stability (review), Jacobean. 2dlinear
5 W X-hr
36 Th2.5(HW2 due) Nonlinear maps, fixed point stability, Henon example.
11 Tu2.6-2.7, Challenge 2Stable/unstable manifolds, disc under linear map `iterdisc2d.m`, periodic orbits on linear map on a torus. manifolds, torus
12 W X-hr
413 Th3.1-3.2(HW3 due) Lyapunov exponents, chaotic orbits, binary. binary
18 Tu3.3, 3.4Conjugacy, 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
520 Th4.1(HW4 due Friday 5pm) Fractals: Cantor sets. applet, difference of two cantor sets.
25 Tu4.2, 4.3(Project choice due). Fractals from tent map, logistic map with a>4. Fractals from probabilistic games. Sierpinski gasket, game 1,2probgames
627 Th4.4-4.5(HW5 due). Julia and Mandelbrot sets, Devaney movies, Fractal dimension.mandel
Nov 1 Tu4.6-4.7 Fractal dimension. Box-counting dimension. Computing box-counting. Correlation dimension boxdim
2 W X-hr
73 Th5.1-5.2, 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 Tu7.3-7.5 Nonlinear systems of ODEs, stability. Motion in potential field. code: potential1d.m. potential
9 W X-hr
810 Th7.6, 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 Tu8.2, 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-
915 Th Hamiltonian mechanics and flows: double pendulum (applets 1, 2), Liouville's Theorem on volume-preservation. liouville
22 TuCh. 13Delay 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 TuStudent project presentations in lecture slot.
30 W X-hrRest of student presentations
102 FrProject write-ups due (noon)
3 Sa - 7 W: Exam period (no final exam :) )