Dynamical Systems
 

 

NEWS

i) Re-examination here at the math dept. in room S2, April 18 from 12 to 16.45.

ii) Course evaluation
(Please, take a moment to fill out this anonymous course evaluation!)

Teacher:
Torbjörn Lundh (examiner 9589), torbjrn@math.chalmers.se, 772 3503.
Course code: FFR 130

Course book: Chaos Theory Thamed (CTT) by
G.P.Williams, Taylor and Francis, 1997.

Williams is a geologist and has an intention to explain
in a basic way a lot of dynamical/chaotic features.

The Auxilary toolkit (pp. 21 - 158) gives a repetition of
the mathematical tools needed as a background.

Homework
Every week there will be a set of problems to be solved in order to get credits for the course.

Written exam
There will be a written exam at the end of the course.
Schedule 
Information of the Master's program

Plan of the future lectures and history of the past:

 Date  Place  Subject CTT
010115 FL 74 Introduction to the course and the book.  1,2
010117 FL 74 Introduction to time series and   repetition of some basic probability theory. 6,7
010122 FL 74 Cont. with time series with some realistic examples and different techniques and concepts such as stationarity, iid, corollogram etc. white noise, random walk. 7,9
010124 FL 74 The AR(1) model, differencing, logarithmic transformations, and two tests for noise. 
010129 FL 74 Sensitive dependence on initial conditions, the logistic map and bifurcations. 14-16
010131 FL 74 Attractors, Poincare sections, rerun maps, and lag-spaces. Homework 2 due date. 18,19
010205 FL 74  How to choose the "right" lag , correlation integral,  and an introduction to the correlation dim. 17,20
010207 FL 74  Natural and deterministic fractals. History of fractals. von Koch's snowflake. A mathematical description of self similar fractals. The 1/3-Cantorset in 1 and 2 dimensions. Self affine fractals and the Hurst exponent. Homework 3 due date. 21,22
010212 FL 74 Different fractal dimensions like the Similarity dimension, Capacity, Hausdorff dimension, and Infromation dimension. The Hurst exponent and 1/f noise.  Observe an added program on the homeworksheet for generating drummer data of your own. 23,24
010214 FL 74 The Correlation dimension. Homework 4 due date. 24
010219 FL 74 The Lyaponov exponent. 25
010221 FL 74 Repetition of some basic Complex analysis (eg. analytic functions, the Riemann sphere, Schwarz lemma etc) .  The Möbius maps.Homework 5 due date.
010226 FL 74 Different classes of fixedpoints, quadratic maps, Fatou-, Julia-, and the Mandelbrot sets. 
010228 FL 74  More examples on the  Julia- and Mandelbrot sets, and limit sets of discrete groups. Summation with the help of  some sample questions in the style of the written exam. A discussion of the so called butterfly effect. Homework 6 due date.  We will also talk about the first and last part of Homework 6, so please hand it in before we do that!
010308  ML 17 Exam 08.45-12.45        New: The exam in ps format; pdf format.

 

 

 
 


Some indicated anwsers to the home work problems:

Homework 2 Answers
Homework 3 Answers
Homework 4 Answers
Homework 5 Answers
Homework 6 Answers