# Math 53: Schedule, topics and worksheets

week  date   readingdaily topics & demosworksheets
1Sep 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 F1.4-1.5Periodic orbits, logistic family of maps, bifurcation diagramperiodic
Oct 1 M1.6-1.7`Periodic table' of logistic map 4x(1-x), sensitive dependence on initial conditionstable
23 Wthisdiscussion/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 F1.8(HW1 due) Itinerariesitineraries
8 M2.1-2.2Poincare section, 2D maps, sinks, sources, saddles
310 W2.3-2.4Linear maps, stability (review), Jacobean 2dlinear
11 Th X-hr
12 F2.5Nonlinear maps, fixed point stability, Henon example.
15 M2.6-2.7Stable/unstable manifolds, disc under linear map `iterdisc2d.m` manifolds
417 WChallenge 2, 3.1Periodic 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 F3.1-3.2Lyapunov exponents, Chaotic orbits.
22 M3.3Binary, conjugacy, uses for logistic mapbinary
Midterm 1: Tues Oct 23, 6-8pm, Silsby 028 (on everything apart from Matlab - note evening + weird location)
524 W3.4 Dense orbits, transition graphs and counting periodic orbitstransgraph
25 Th X-hr
26 F4.1, 4.3 Fractals: Cantor sets, fractals from tent map, logistic map with a>4. applet, difference of two cantor sets.
29 M4.2fractals from probabilistic games. Sierpinski gasket, game 1,2probgames
631 W4.4Project choice due. Julia and Mandelbrot sets Devaney movies
Nov 2 F4.5 Fractal dimension. Box-counting dimension.
5 M4.6-4.7 Computing box-counting. Correlation dimensionboxdim
77 W(lecture postponed to Thurs X-hr)
8 Th X-hr7.3-7.4Flows: linear (review) and nonlinear systems of ODEs, stability.
9 Fr7.5Motion in potential field. code: potential1d.m
12 M7.5-7.6More motion in potential field, damping, damped pendulum potential
814 W7.6, Ch.9Project 2-page descriptions due. Lyapunov functions.
15 Th X-hrReview session
Midterm 2: Thurs Nov 15, 6-8pm, Silsby 028 (note evening + weird location)
16 Fr8.1, 8.2Range of flow limit behaviors in R and R2: Poincare-Bendixson theorem. Chaos in ODEs: Lorenz attractor.
19 M5.1, 5.2, 9.6Lyapunov exponent for maps in Rn and flows: numerical measurement, lyap2d, lyapflow (needs lorenz_time1map.m)
.................................. Nov 21 W - 25 Su Thanksgiving recess ...............................
926 MCh. 13Delay embedding henon_timedelay.m.
28 WHamiltonian mechanics and flows: double pendulum (applets 1, 2), billiards
29 Th X-hrLiouville's Theorem on volume-preservation. Autocorrelation of time-series (henon_autoc.m) liouville
30 F(no lecture - Alex out of town)
10Dec 3 MProject Presentations in lecture, continue in evening (6-8pm) with pizza.
5 W(no lecture)
6 ThProject write-ups due (noon).
7 Fr - 11 Tu: Exam period (no final exam)