The lecture notes for my related masters level course Introduction to
Dynamical Systems might also be helpful. In case you are interested, see
the course webpage.
Final exam
Take-home exam, see regulations of LTCC.
Literature
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:
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)