Homepage for Bifurcations and Chaos 2014
This course is concerned with the application of methods from
dynamical systems and bifurcation theories to the study of nonlinear
oscillations. The mathematical models we consider are (fairly small)
sets of ordinary differential equations and mappings. As examples we
look at nonlinear oscillations: the famous oscillators of van der Pol
and Duffing, the Lorenz equations, and a bouncing ball problem. We show
that the solutions of these problems can be markedly chaotic and that
they seem to possess strange attractors: attracting motions which are
neither periodic nor quasiperiodic. In order to develop the idea of
chaos, we discuss the Smale horseshoe map and describe the method of
symbolic dynamics. Moreover, we analyse global homoclinic and
heteroclinic bifurcations and illustrate the results with the examples
of the nonlinear oscillators.
Literature: Nonlinear oscillations, dynamical systems, and
bifurcations of vector fields. Applied Mathematical Sciences,
J. Guckenheimer, P. Holmes, Vol. 42, Springer-Verlag, New
York, 1983, ISBN 0-3879-0819-6
Instructor: Vivi Rottschäfer
Office: 206
Assistent: Corine Meerman
Email: cmeerman[at]math.leidenuniv.nl
Office: 204
Assignments:
Assignment Set 1
Deadline: 17 March 2014, 17:00
Assignment Set 2
Deadline: 7 April 2014, 17:00
Assignment Set 3
Deadline: 12 May 2014, 17:00
The deadlines for the assignments are strict!
Lecture schedule:
6 Feb
|
2.2, 1.5
(Poincare map intermezzo)
|
| 13 Feb |
2.2 (cont.),
4.1
|
| 20 Feb |
4.1 (cont.),
4.2
|
| 27 Feb |
4.3, 4.5
|
6 March
|
|
| 13 March |
no class |
| 20 March |
|
| 27 March |
|
3 April
|
|
| 10 April |
|
| 17 April |
no class |
| 24 April |
? no class |
| 1 May |
|
8 May
|
|
| 15 May |
|
| 21 May |
|