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
- 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...
