Homepage for Bifurcations and Chaos 2018
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, SpringerVerlag, New York, 1983, ISBN
0387908196
Instructor: Vivi Rottschäfer
Office: 206
Assistent: Olfa Jaïbi
Email: o.jaibi[at]math.leidenuniv.nl
Assignments:
Assignment Set 1
Deadline: 22 March 2018,
11:00
The deadlines for the assignments are strict!
Lecture schedule:
8 Feb

2.2, 1.5
(Poincare map intermezzo)

15 Feb 
2.2
(cont.), 4.1

22 Feb 
4.1
(cont.), 4.2

22 Feb 
4.3, 4.5

1 March


8 March 

15 March 
no class 
22 March 

29 March

no class

5 April 

12 April 

19 April 
no class 
26 April 

3 May


10 May 
no class 
17 May 

24 May

