## MAS424/MTHM021 |
## Introduction to Dynamical Systems |

Course Material |
Fall 2007 |

- Course organiser

Rainer Klages; office hours: upon appointment

- College web pages
College course directory Maths UG Handbook - Timetable

time room lectures

Thu 10.00-12.00

G2

optional exercise class

Thu 12.00-13.00

G2

- Exercise sheets
number hand out

solution

on the web

model

solution

sheet 1

05/10

2/11

solution 1

sheet 2

1/11

15/11

solution 2 sheet 3

15/11

28/11

solution 3

sheet 4

29/11

13/12

solution 4

- Lecture
notes

A fully worked-out set of lecture notes is available here.

- Lecture regulations

Students are expected to attend every lecture. Registers of attendance will be taken in lectures on a random basis.

- Coursework regulations

There will be four problem sheets during this course, see also the links included above. This coursework does not count to your final mark, and I won't mark your solutions. Two to three weeks after I handed out the problem sheets I will put model solutions on this webpage. In case of any questions or difficulties I will be happy to discuss your coursework with you during the optional exercise classes.

It is highly recommended that you do all the coursework problems! You won't have a chance to pass your final exam with a reasonable grade without doing all the suggested exercises. - Final exam

A final list of key objectives to be mastered in order to be reasonably sure of passing the examination in this course with a reasonable grade you can find here. **Literature**
Your course notes should be sufficient. However, it would
be very useful to look, for example, into the following books for
further details (1-3 and 6 are available in the short loan collection
of the library):
- R.L. Devaney, An Introduction to Chaotic Dynamical Systems (Westview Press, 2003) (nice outline of basic mathematics concerning low-dimensional discrete dynamical systems)
- K.T. Alligood, T.D. Sauer, J.A. Yorke, Chaos (Springer, 1996) (easy introduction from a more mathematical point of view)
- B. Hasselblatt, A. Katok, A
First Course in Dynamics (Cambridge
Univ Press, 2003) (bridges the gap towards Katok/Hasselblatt's `bible'
on dynamical systems theory, see 8.)

- C. Robinson, Dynamical
Systems (CRC Press, London, 1995) (more advanced introduction
from a more mathematical side)

- E. Ott, Chaos in Dynamical Systems (Cambridge Univ Press, 1993) (easy introduction from a more applied point of view)
- C. Beck, F. Schloegl, Thermodynamics of Chaotic Systems: An Introduction (Cambridge University Press, 1995) (a very useful supplement)
- A. Lasota, M.C. Mackey, Chaos,
Fractals, and Noise (Springer, 1994) (describes the
probabilistic approach to dynamical systems, cf. part on measures and
pdf's in this course)

- J.R. Dorfman, An Introduction to Chaos in Nonequilibrium Statistical Mechanics (Cambridge, 1999) (applies dynamical systems theory to statistical mechanics; for this lecture focus on the dynamical systems aspects only)
- A. Katok, B. Hasselblatt, Introduction
to the Modern Theory of
Dynamical Systems (Cambridge, 1995) (detailed summary of the
mathematical foundations of dynamical systems theory (800 pages!) - too
advanced for this course, but important for further studies)

- L. Smith, Chaos - A very short introduction (Oxford, 2007) (very nice short introduction to nonlinear dynamics, presented within the general socio-cultural context)
- J. Gleick, Chaos - making a new science (Penguin, 1995) (one of the classic popular science books on chaos)
- H.E. Nusse, J.A. Yorke, Dynamics: Numerical Explorations (Springer, 1997) (This is a handbook with software package that enables the computation of many dynamical systems properties for given nonlinear equations of motion)
- see the lecture
notes for the follow-up 1st year Ph.D. course on Applied Dynamical
Systems

- Caltech class Introduction to Chaos with lecture notes and numerical demonstrations, see particularly the applet of various one-dimensional maps producing cobweb plots.
- The Pendulum Lab - a very nice virtual laboratory, where you can explore the chaotic dynamics of various nonlinear driven pendulums (cf. one of the demonstrations in this course)
- if all of this is not challenging enough for you: try the Chaos Book

- interested in research on these topics? see Dynamical Systems at Queen Mary
- Further information

The 2005 exam paper you can find here.

The exam papers for 2006 and 2007 you can find here (see link under MAS424, Intro to Dyn. Sys.)