week | date | reading | daily topics & demos | worksheets |
---|---|---|---|---|

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 R: Poincare-Bendixson theorem.
Chaos in ODEs: Lorenz attractor.
^{2} | ||

19 M | 5.1, 5.2, 9.6 | Lyapunov exponent
for maps in R and flows: numerical measurement,
lyap2d,
lyapflow (needs
lorenz_time1map.m)
^{n} | ||

.................................. 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) |