# Math 53, FALL 2015: Schedule, topics and worksheets

week   date    readingdaily topics & demosworksheets
1Sep 17 Th Intro, 1.1-1.4 Discrete maps, fixed points, stability, cobweb plot. Periodic orbits. cobweb, periodic
22 Tu1.5-1.7Logistic family of maps, bifurcation diagram, `Periodic table' of logistic map 4x(1-x), sensitive dependence on initial conditionstable
23 W X-hrintro53.m Matlab technique (by now you'll have installed it; bring your laptop)
224 Th1.8, 2.1(HW1 due) Itineraries and subinterval ordering, (proof of small subintervals) itineraries
26 Sa2.2-2.4Poincare section, 2D maps, sinks, sources, saddles, linear maps, stability (review), Jacobean. 2dlinear
29 Tu2.5 Nonlinear maps, fixed point stability, Henon example (henon_bifurc_anim.m).
30 W X-hr
3Oct 1 Th2.6-2.7, Challenge 2 (HW2 due) Stable/unstable manifolds, disc under linear map iterdisc2d.m, periodic orbits on linear map on a torus. manifolds, torus
6 Tu3.1-3.2 Lyapunov exponents, chaotic orbits, binary. binary
7 W X-hr
48 Th3.3, 3.4 (HW3 due) Conjugacy, uses for logistic map, dense orbits, transition graphs and counting periodic orbits. transgraph
13 Tu4.1 Fractals: Cantor sets. applet, difference of two cantor sets.
14 W X-hrmidterm review
Midterm 1: Wed Oct 14, 6-8pm, Hald 028 (usual room). On: everything up to and including 3.1, apart from Matlab.
515 Th4.2, 4.3 (HW4 due Fri) Fractals from probabilistic games. Sierpinski gasket, game 1,2; IFS. Fractals from tent map, logistic map with a>4. probgames,
20 Tu4.4-4.5 (Project choice due; discuss/email). Julia and Mandelbrot sets, Julia applet, Devaney movie.mandel
21 WX-hr
622 Th4.6-4.7 (HW5 due). Fractal dimension. Box-counting dimension. Computing box-counting. boxdim
27 Tu5.1-5.2, 7.1-7.2 (Project 1-2 page plan with references due). Correlation dimension. Lyapunov exponent for maps in Rn and their numerical measurement, lyap2d. Flows: linear (review).
28 WX-hr
729 Th7.3-7.5 (HW6 due). Nonlinear systems of ODEs, stability. Motion in potential field. code: potential1d.m. potential
Nov 3 Tu7.6, Ch.9, 8.1 Damping in potential field, damped pendulum. Lyapunov functions. Range of flow limit behaviors in R and R2: Poincare-Bendixson theorem.
4 W X-hrreview for midterm 2
85 Th8.2, 9.6 (HW7 due) Chaos in ODEs: Lorenz attractor (applet). Measuring Lyapunov exponent in flows lyapflow (needs lorenz_time1map.m)
Midterm 2: Mon Nov 9, 6-8pm, Hald 028 (usual room). On: everything since Midterm 1 up to damping in potential field. (solutions)
10 Tu Hamiltonian mechanics and flows: double pendulum (applets 1, 2), notes on Hamiltonian mechanics, equations for double pendulum. Liouville's Theorem on volume-preservation. liouville
11 W X-hr-
912 ThCh. 13Integrable/chaotic Hamiltonian systems. Time-delay embedding, timedelaydemo, needs the four time-series made by make_timeseries.
17 TuStudent project presentations in lecture slot.
18 W X-hrRemaining student presentations
23 M9am. Project write-ups due.
20 Fr - 25 W: Exam period (we have no final exam :) )