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

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