Professor Erik Bollt, Fall 2005

MA563– Graduate Applied Dynamical Systems - Yup...that includes Chaos.

NEW! HW Solutions to previous problems on reserve at the library website:

Course Policy Statement MA563CoursePolicyF05.pdf
Syllabus
Office Hours OfficeHoursFall05.htm
Homework-Download
- Homework 1 and some useful handouts
- ATTENTION!!! Some of the problems say "Read Carefully" That means that you DO NOT have to do the problems, but I am only asking that you read the question.
- - Download 1 about Maple in general.
  - Download 2 how to Picard iterate a function, or as a pdf
  - Download 3 how to use Maple to numerically graph a solution of a one-d ODE, and its vector field, or as pdf
  - A help sheet from Colorado about how to find generalized eigenvectors and how to use them in ODEs pdf
- Homework 2 Part 1 and Homework 2 Part 2.
- - Download a code in Matlab to plot stable and unstable manifolds of the Henon map, for part 1e. (Other parts to be done in closed form).
  - Download some matlab code to help you make a stroboscopic map of the Duffing oscillator.
    - iter.m runs the supporting subroutines. Note that you will need to change the loop to have i=1:50,000 to make the pretty picture shown in the handout, but that will take your poor comuter a long time to run
    - dydtDuff.m this is the matlab's rendition of the vector field -the right hand side of the ODE. Take a very close look for your future reference.
    - duffmap.m this evolves the flow, numerically, for one stroboscopic period. Take a close look and see odeset and ode45 in particular
  - Download some matlab code to help you make a stroboscopic map of the Duffing oscillator.
    - LorenzT.m Compute and plot solutions of Lorenz equations. Try typing Lorenzt([1 2 3],100] to see a solution evolve from that initial condition until time t=100.
    - dydtLorenz.m The Lorenz vector field called by LorenzT
  - Download some matlab code to help you make the discrete time successive maxima map for the Lorenz equations flow.
    - LorenzMapIterators.m Code to produce the Lorenz successive maxima map empirically. Simply type LorenzMapIterator
    - And supporting code, the vector field LorenzEqns.m, and the code LorenzMap.m which maps forward until next maxima in the z-coordinate. Notice the event stopping code.
- Homework 3
- Homework 6
- Homework 7 and some useful code for problem 7 to compute the box counting dimension of a sampled orbit segment, such as one you compute from the Henon map as asked.