Ideas for projects

Here follows a first list of possible directions for projects:

• Approximation of invariant measures with Ulam's method (suggested starting point: Ding & Zhou, chapter 6/7)
• Ergodic decomposition (suggested starting point: Viana & Oliveira, chapter 5, and M. Klünger's lecture notes)
• Decay of correlations (suggested starting point: Viana & Oliveira, chapter 7)
• Entropy (suggested starting point: Viana & Oliveira, chapter 9)
• Ergodic theory of chaotic billiards (suggested starting point: Chernov & Markarian)
• Lyapunov exponents and Oseledets multiplicative ergodic theorem (suggested starting point: Viana)
• Conditionally invariant measures
  (suggested starting point: M.F. Demers and L.-S. Young, Escape rates and conditionally invariant measures, Nonlinearity 19 (2006) 377–397 doi:10.1088/0951-7715/19/2/008

Or other topics from the books

• A. Boyarsky and P. Gora. Laws of chaos (1997)
• N. Chernov and R. Markarian. Chaotic billiards (2006)
• J. Ding and A. Zhou, Statistical properties of deterministic systems (2009)
• A. Lasota and  M. Mackey, Chaos, Fractals and Noise (1994) 
• M. Viana and K. Oliveira. Foundations of ergodic theory (2016)
• M. Viana. Lectures on Lyapunov exponents (2014)

Or anything else you may find of interest...

Material covered 30/1

We completed the lecture notes material of Chapter 3, and reached Chapter 4 until proposition 4.3 on page 24.

Material covered 23/1

We completed the lecture notes material of Chapter 2, and reached Chapter 3 until subsection 3 on page 18.

Material covered 16/1

We discussed lecture notes material Chapter 1, until subsection 6 on page 9.

Lectures tuesdays 11:00-13:00

The lectures for Ergodic Theory will be on tuesdays, 11:00-13:00 in my office (Huxley 638), starting tuesday 16 January. The lectures will initially follow the 2017 lecture notes of Martin Rasmussen (that can be downloaded from right-hand side margin). My rough aim is to cover 10-20 pages per lecture. It is advisable to read ahead in advance of the lecture. I will note the material we covered after each lecture.

Time table

I have just become aware of the fact that there are 3 contact hours scheduled in the official time-table for this course. This has happened without my knowledge. In previous years no rooms were booked for this course. We discuss the schedule of lectures and meetings on Fri 12 January, 12pm in room 638.

First meeting, 12pm on Friday 12 January in Huxley 638

Students interested in taking this course are advised to contact me (jeroen.lamb@imperial.ac.uk). There will be a first meeting on Friday 12 January 2017 at 12pm in my office (Huxley 638) where the course material and the scheduling of the weekly meetings will be discussed.