Homepage for Bifurcations and Chaos 2016
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: Christian Hamster
Email: chamster[at]math.leidenuniv.nl
Course: time has changed compared to original
schedule,
the course is now on Mondays from 13:45-15:30 in
room 408 during 15 Feb until 29 Feb and
in room 402 during 14 March until 23 May
Assignments:
Assignment Set 1
Deadline: 14 March 2016,
13:45
Assignment Set 2
Deadline: 11 April 2016,
13:45
Assignment Set 3
Deadline: 2 May 2016, 13:45
Assignment Set 4
Deadline: 30 May 2016, 13:45
Assignment Set 5
Deadline: 20 June 2016, 13:45
The deadlines for the assignments are strict!
Lecture schedule:
1 Feb
|
2.2, 1.5
(Poincare map intermezzo)
|
| 8 Feb |
2.2
(cont.), 4.1
|
| 15 Feb |
4.1
(cont.), 4.2
|
| 22 Feb |
4.3, 4.5
|
29 Feb
|
|
| 7 March |
no class |
| 14 March |
|
| 21 March |
|
28 March
|
no class
|
| 4 April |
|
| 11 April |
no class |
| 18 April |
|
| 25 April |
|
2 May
|
|
| 9 May |
|
| 16 May |
no class |
23 May
|
|