Dynamical properties of commuting automorphisms
Thomas Ward
Abstract.
These lectures will be a gentle introduction
to some of the main themes and results in the
dynamical properties of commuting automorphisms.
This subject is a rich source of examples and ideas
in ergodic theory, and there is a strong dialogue
between it and number theory. Much of the theory
has been developed by Prof. Klaus Schmidt.
Tentative list of topics:
- Algebraic dynamical systems
- Ergodicity and mixing
- Expansiveness
- Entropy & Lehmer's problem
- Mixing and S-units
- Growth in entropy rank one and Baker's theorem
- Joinings
Background assumed:
Some of Walters "An introduction
to ergodic theory", basics of
Fourier analysis on compact abelian groups,
modest commutative algebra.