Applied Dynamical Systems

Course Material Spring 2010

  1. Course organisers
    for Part 1 (Lectures 1 - 4): Wolfram Just
    for Part 2 (Lectures 5 - 10): Rainer Klages; for office hours please see my homepage

  2. Official web pages
    London Taught Course Centre

  3. Timetable
    Lectures will take place in De Morgan House on Mondays, 15.30h-17.30h from 01/03 to 29/3/2010.
  4. Exercises
    note: working through these exercises will help you to prepare for the exam.

  5. Lecture notes

  6. Final exam
    Take-home exam, see regulations of LTCC.

  7. Literature
  8. For Part 2: your course notes should be sufficient. However, it would be very useful to look, for example, into the following books for further details:
    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)

  9. Further information
last update: 30 March 2010