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

1 | Sep 17 Th | Intro, 1.1-1.4 | Discrete maps, fixed points, stability, cobweb plot. Periodic orbits. | cobweb, periodic |

22 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 | |

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

2 | 24 Th | 1.8, 2.1 | (HW1 due) Itineraries
and subinterval ordering,
(proof of small subintervals)
| itineraries |

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

29 Tu | 2.5 |
Nonlinear maps, fixed point stability, Henon example
(`henon_bifurc_anim.m` ).
| ||

30 W X-hr | ||||

3 | Oct 1 Th | 2.6-2.7, Challenge 2 |
(HW2 due)
Stable/unstable manifolds, disc under linear map `iterdisc2d.m` , periodic orbits on linear map on a torus.
| manifolds, torus |

6 Tu | 3.1-3.2 | Lyapunov exponents, chaotic orbits, binary. | binary | |

7 W X-hr | ||||

4 | 8 Th | 3.3, 3.4 |
(HW3 due)
Conjugacy, uses for logistic map, dense orbits,
transition graphs and counting periodic orbits.
| transgraph |

13 Tu | 4.1 | Fractals: Cantor sets. applet, difference of two cantor sets. | ||

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

Midterm 1: Wed Oct 14, 6-8pm, Hald 028 (usual room).
On: everything up to and including 3.1, apart from Matlab.
| ||||

5 | 15 Th | 4.2, 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 Tu | 4.4-4.5 |
(Project choice due; discuss/email).
Julia and Mandelbrot sets,
Julia applet,
Devaney movie. | mandel | |

21 WX-hr
| ||||

6 | 22 Th | 4.6-4.7 |
(HW5 due).
Fractal dimension. Box-counting dimension.
Computing box-counting.
| boxdim |

27 Tu | 5.1-5.2, 7.1-7.2 |
(Project 1-2 page plan with references due).
Correlation dimension.
Lyapunov exponent
for maps in R and their numerical measurement,
lyap2d.
Flows: linear (review).
^{n} | ||

28 WX-hr
| ||||

7 | 29 Th | 7.3-7.5 |
(HW6 due).
Nonlinear systems of ODEs, stability.
Motion in potential field.
code: potential1d.m.
| potential |

Nov 3 Tu | 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} | ||

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

8 | 5 Th | 8.2, 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 | -
| |||

9 | 12 Th | Ch. 13 | Integrable/chaotic Hamiltonian systems. Time-delay embedding, timedelaydemo, needs the four time-series made by make_timeseries. | |

17 Tu | Student project presentations in lecture slot. | |||

18 W X-hr | Remaining student presentations | |||

23 M | 9am. Project write-ups due. | |||

20 Fr - 25 W: Exam period (we have no final exam :) ) |