MTH715U/MTHM021: Introduction to Dynamical Systems

  1. Official web page
    Maths UG Handbook

  2. Timetable
    time room
    Thu. 11:00-12:00 M 203
    Thu. 12:00-13:00 M 203
    Thu. 15:00-16:00 M 103 (tutorial)
    Fri. 13:00-14:00 M 513 (tutorial)

  3. Office hours (during teaching semesters)
    Mon. 14:00-15:00
    Tue. 14:00-15:00
    Wed. 14:00-15:00
    Thu. 14:00-15:00
    Fri. 14:00-15:00
    (you can try other times as well. If not in: please contact me by email)

  4. Lecture notes / problem sheets / marking schemes
    <
    no. due to solutions lecture notes
    week 1 sheet 1 N/A solution notes
    week 2 sheet 2 N/A solution notes
    week 3 sheet 3 N/A solution notes
    week 4 sheet 4 N/A solution notes
    week 5 sheet 5 N/A solution notes
    week 6 sheet 6 N/A solution notes
    week 7 sheet 7 N/A solution notes
    week 8 sheet 8 N/A solution notes
    week 9 sheet 9 N/A solution notes
    week 10 sheet 10 N/A solution notes
    week 11 sheet 11 N/A solution notes
    week 12 - - - notes

  5. Literature
    There are plenty of textbooks on dynamical systems covering various aspects. The two listed below are just examples which address the physics and the pure mathematical side of the topic, respectively:
    There exists a nice reading list from Rainer Klages (from a previous course):
    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

  6. Questionnaire: statistics

  7. Final exam

  8. Key objectives
    To pass the exam, you must be able:

  9. Rubric
    You should attempt all questions. Marks awarded are shown next to the question.
    (that means: calculators are NOT permitted in this examination)

  10. Assessment ratio splits
    100% final exam