Introduction to Dynamical Systems

Course Material Fall 2007

  1. Course organiser
    Rainer Klages; office hours: upon appointment

  2. College web pages
    College course directory
    Maths UG Handbook

  3. Timetable

    time room
    Thu 10.00-12.00
    optional exercise class
    Thu 12.00-13.00

  4. Exercise sheets
    number hand out
    on the web
    sheet 1
    solution 1
    sheet 2
    solution 2
    sheet 3
    solution 3
    sheet 4
    solution 4

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

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

  7. 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.

  8. 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.
    The final exam will take place on Friday, 9 May 2008, 10:00. Its duration will be three hours. The rubric will state: You should attempt all questions. Marks awarded are shown next to the questions. Calculators are NOT permitted in this examination. Assessment: The final exam counts 100% for your final mark of this course.
    Please note: I will not hand out model solutions for past exams. All solutions to previous exams are either in your lecture notes or in your coursework solutions. I will be available for answering specific questions during my office hours.
    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.)

  9. Literature
  10. 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):
    1. R.L. Devaney, An Introduction to Chaotic Dynamical Systems (Westview Press, 2003) (nice outline of basic mathematics concerning low-dimensional discrete dynamical systems)
    2. K.T. Alligood, T.D. Sauer, J.A. Yorke, Chaos (Springer, 1996) (easy introduction from a more mathematical point of view)
    3. 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.)
    4. C. Robinson, Dynamical Systems (CRC Press, London, 1995) (more advanced introduction from a more mathematical side)
    5. E. Ott, Chaos in Dynamical Systems (Cambridge Univ Press, 1993) (easy introduction from a more applied point of view)
    6. C. Beck, F. Schloegl, Thermodynamics of Chaotic Systems: An Introduction (Cambridge University Press, 1995) (a very useful supplement)
    7. 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)
    8. 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)
    9. 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)
    some bedtime reading:
    1. L. Smith, Chaos - A very short introduction (Oxford, 2007) (very nice short introduction to nonlinear dynamics, presented within the general socio-cultural context)
    2. J. Gleick, Chaos - making a new science (Penguin, 1995) (one of the classic popular science books on chaos)
    numerical explorations:
    1. 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)
    if you want to get further into the matter:
    1. see the lecture notes for the follow-up 1st year Ph.D. course on Applied Dynamical Systems
    2. Caltech class Introduction to Chaos with lecture notes and numerical demonstrations, see particularly the applet of  various one-dimensional maps producing cobweb plots.
    3. 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)
    4. if all of this is not challenging enough for you: try the Chaos Book
    5. interested in research on these topics? see Dynamical Systems at Queen Mary

  11. Further information
last update: 18 April 2008