The lectures (in term 2) are: Tuesday 16-17 (MS.04); Wednesday 12-13 (B3.03); Thursday 14-15 (B3.03).
An important prerequisite is measure theory.
Here is an informal summary of
those topics it would be useful to know:
Summary of measure theory
Below are scans of my hand written lecture notes (often corrected as the
course progressed)
lecture 1 (Overview)
lecture 2 (Invariant measures, Examples, Existance)
lecture 3 (Poincare Recurrence Theorem,
Multiple Recurrence, Geodesic and horocycle flows)
lecture 4 (Ergodic measures, Examples, Existance)
lecture 5 (Kac's Theorem, von Neumann Ergodic Theorem)
lecture 6 (Birkhoff Ergodic Theorem)
lecture 7 (Subadditive ergodic theorem)
lecture 8 (Ergodicity of flows and Hopf
method)
lecture 9 (Spectral Theory)
lecture 9.5 (Entropy)
lecture 10 (SMB theorem. OW theorem)
lecture 11 (Markov operators and
Dunford-Schwartz-Hopf Ergodic Theorem)
lecture 12 (Pressure and equilibrium states)
Below are additional references
Paper of Kaznelson-Weiss: Short proof of
ergodic theorem (L^1 functions and invariant measures)
Appendix of Parry
book: Proof of spectral theorems
Below are typed lecture notes (often corrected as the
course progressed)
lecture Notes: First part
lecture Notes: Second part
lecture Notes: All the notes
Example and Solution sheets:
Example sheet 1;
Example sheet 2;
Example sheet 3;
Example sheet 4;
Example sheet 5; ... Probably to be revised
Example sheet 6;
Example sheet 7;
Example sheet 8;
Solution sheet 1;
Solution sheet 2;
Solution sheet 3;
Solution sheet 4;
The lectures (in term 2) are: Monday 9-10 (H.0.51); Wednesday 9-10 (MS.01); Friday 10-11 (H0.51).
Below are scans of my hand written lecture notes (often corrected as the
course progressed)
lecture Notes 1 (Overview)
lecture Notes 2 (Mobius maps)
lecture Notes 3 (Applications of Mobius maps) and
an article by Sarnak on
Circle packings
lecture Notes 4 (Analyticity, Cauchy-Riemann equations)
lecture Notes 5 (Application:Non-acculumulation
of zeros)
lecture Notes 6 (Integrals, Theorems of Gousart
and Cauchy) (Correction)
lecture Notes 7 (Applications of Theorems of
Gousart and Cauchy)
lecture Notes 8 (Properties of Analytic
functions:Arg and Log)
lecture Notes 9 (Location of zeros: Argument
Principle and Rouche's Theorem)
lecture Notes 10 (Weierstrauss-Hurwicz theorem,
Liouville theorem)
lecture Notes 11 (Montel's Theorem)
lecture Notes 12 (Riemann Mapping Theorem)
lecture Notes 13 (Schwarz-Christoffel Theorem,
Schwarz Reflection Principle, Osgood Caratheodory Theorem)
lecture Notes 14 (Harmonic functions)
Example and Solution sheets:
Example sheet 1
Example sheet 2
Example sheet 3
Example sheet 4
Example sheet 5
Example sheet 6
Solution sheet 1
Solution sheet 2
(TA's solutions)
Solution sheet 3
(TA's solutions)
Solution sheet 5 (TA's solutions)
Solution sheet 6 (TA's solutions)
Solution sheet 7 (TA's solutions)