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

1 | Sep 22 Th | Intro, 1.1-1.4 | Discrete maps, fixed points, stability, cobweb plot. Periodic orbits. | cobweb, periodic |

27 Tu | 1.5-1.7 | Logistic family of maps,
bifurcation diagram, `Periodic table' of logistic map 4x(1-x),
sensitive dependence on initial conditions | table | |

28 W X-hr | `intro53.m`
| Matlab technique (by now you'll have installed it; bring your laptop) | ||

2 | 29 Th | 1.8, 2.1 | (HW1 due) Itineraries
(proof of small subintervals)
| itineraries |

Oct 4 Tu | 2.2-2.4 | Poincare section, 2D maps, sinks, sources, saddles, linear maps, stability (review), Jacobean. | 2dlinear | |

5 W X-hr | ||||

3 | 6 Th | 2.5 | (HW2 due) Nonlinear maps, fixed point stability, Henon example.
| |

11 Tu | 2.6-2.7, Challenge 2 | Stable/unstable manifolds, disc under linear map `iterdisc2d.m` , periodic orbits on linear map on a torus.
| manifolds, torus | |

12 W X-hr | ||||

4 | 13 Th | 3.1-3.2 | (HW3 due) Lyapunov exponents, chaotic orbits,
binary.
| binary |

18 Tu | 3.3, 3.4 | Conjugacy, 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 | ||||

5 | 20 Th | 4.1 | (HW4 due Friday 5pm) Fractals: Cantor sets.
applet, difference of two cantor sets.
| |

25 Tu | 4.2, 4.3 | (Project choice due). Fractals from tent map,
logistic map with a>4. Fractals from probabilistic games.
Sierpinski
gasket, game 1,2 | probgames | |

6 | 27 Th | 4.4-4.5 | (HW5 due). Julia and Mandelbrot sets,
Devaney movies, Fractal dimension. | mandel |

Nov 1 Tu | 4.6-4.7 | Fractal dimension. Box-counting dimension. Computing box-counting. Correlation dimension | boxdim | |

2 W X-hr
| ||||

7 | 3 Th | 5.1-5.2, 7.1-7.2 | (HW6 due)
Lyapunov exponent
for maps in R and their numerical measurement,
lyap2d.
Flows: linear (review).
^{n} | |

4 Fr | (Project 1-2 page description due).
| |||

8 Tu | 7.3-7.5 | Nonlinear systems of ODEs, stability. Motion in potential field. code: potential1d.m. | potential | |

9 W X-hr | ||||

8 | 10 Th | 7.6, Ch.9, 8.1 | (HW7 due)
Damping in potential field,
damped pendulum.
Lyapunov functions. Range of flow limit behaviors in
R and R: Poincare-Bendixson theorem.
^{2} | |

15 Tu | 8.2, 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 | -
| |||

9 | 15 Th | Hamiltonian mechanics and flows: double pendulum (applets 1, 2), Liouville's Theorem on volume-preservation. | liouville | |

22 Tu | Ch. 13 | Delay 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 Tu | Student project presentations in lecture slot. | |||

30 W X-hr | Rest of student presentations | |||

10 | 2 Fr | Project write-ups due (noon) | ||

3 Sa - 7 W: Exam period (no final exam :) ) |