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

1 | Sep 24 Th | Intro, 1.1-1.4 | Discrete maps, fixed points, stability, cobweb plot. Periodic orbits. | cobweb, periodic |

29 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 | |

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

2 | Oct 1 Th | 1.8, 2.1 | (HW1 due) Itineraries
(proof of small subintervals)
| itineraries |

6 Tu | 2.2-2.4 | Poincare section, 2D maps, sinks, sources, saddles, linear maps, stability (review), Jacobean.
[if you need it, 4-5:30pm Intro to Matlab class, Berry Instr Ctr; sign-up reqd]
| 2dlinear | |

7 W X-hr | - | |||

3 | 8 Th | 2.5 | Nonlinear maps, fixed point stability, Henon example. | |

13 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 | |

14 W X-hr | midterm review
| |||

4 | 15 Th | 3.1-3.2 | Lyapunov exponents, chaotic orbits. | torus |

20 Tu | (lecture moved to Wed X-hr)
| |||

21 Wed X-hr | 3.3 | Binary, conjugacy, uses for logistic map | binary | |

Midterm 1: Wed Oct 21, 6-8pm, Kemeny 007 (solutions),
practise exam (solutions)
On: everything up to and including 3.1, apart from Matlab.
| ||||

5 | 22 Th | 3.4, 4.1 | Dense orbits, transition graphs and counting periodic orbits. Fractals: Cantor sets. applet, difference of two cantor sets. | transgraph |

27 Tu | 4.3, 4.2 | Fractals from tent map,
logistic map with a>4. Fractals from probabilistic games.
Sierpinski
gasket, game 1,2 | probgames | |

6 | 29 Th | 4.4-4.5 | (Project choice due Fri). Julia and Mandelbrot sets,
Devaney movies, Fractal dimension. | mandel |

Nov 3 Tu | 4.6-4.7 | Fractal dimension. Box-counting dimension. Computing box-counting. Correlation dimension | boxdim | |

4 W X-hr
| ||||

7 | 5 Th | 5.1-5.2, 7.1-7.2 |
Lyapunov exponent
for maps in R and their numerical measurement,
lyap2d.
Flows: linear (review).
^{n} | |

10 Tu | 7.3-7.5 | Project 2-page descriptions due.
Nonlinear systems of ODEs, stability.
Motion in potential field.
code: potential1d.m.
| potential | |

11 W X-hr | review for midterm 2
| |||

8 | 12 Th | 7.6, Ch.9, 8.1 |
Damping in potential field,
damped pendulum.
Lyapunov functions. Range of flow limit behaviors in
R and R: Poincare-Bendixson theorem.
^{2} | |

17 Tu | 8.2, 9.6 | Chaos in ODEs: Lorenz attractor. Measuring Lyapunov exponent in flows lyapflow (needs lorenz_time1map.m) | ||

18 W X-hr | last-minute review
| |||

Midterm 2: Wed Nov 18, 6-8pm,
Kemeny 007 (solutions),
practise exam (solutions)
| ||||

9 | 19 Th | Ch. 13 | Delay embedding henon_timedelay.m. Hamiltonian mechanics and flows: double pendulum (applets 1, 2), Liouville's Theorem on volume-preservation. Autocorrelation of time-series (henon_autoc.m) | liouville |

24 Tu |
(no lecture)
| |||

.................................. Nov 25 W - 29 Su Thanksgiving recess...............................
| ||||

Dec 1 Tu | Project Presentations in lecture slot. | |||

2 W X-hr | Rest of presentations | |||

10 | 4 Fr | Project write-ups due (noon) | ||

5 Sa - 9 W: Exam period (no final exam) |