Level: MSc
Title: Ergodic optimization
Supervisor:

Prof. Oliver Jenkinson
Research Area: Dynamical Systems and Statistical Physics
Description:

Ergodic theory is concerned with time averages; more precisely, the value of a function when averaged over orbits of a dynamical system. Ergodic optimization deals with those orbits along which time averages are as large as possible, or those invariant measures which maximize the space average.

 

The project will involve identifying maximizing invariant measures for certain dynamical systems and real-valued functions. It may involve exploring connections with certain partial orders on invariant measures induced by stochastic dominance.
Further Reading:
  • P. Walters, An introduction to ergodic theory. Springer, New York, 1980.
  • V. Anagnostopoulou and O. Jenkinson, Which beta-shifts have a largest invariant measure?, Journal of the London Mathematical Society 79 (2009) 445–464.
  • O. Jenkinson, Ergodic optimization, Discrete & Continuous Dynamical Systems 15 (2006) 197–224.
Key Modules:

MTHM007 Measure Theory and Probability

MTH744P Dynamical Systems
Other Information:

This project may be co-supervised by Dr Vasso Anagnostopoulou. Computer programming experience is desirable.
Current Availability: Yes