Time and Place:
- The notion of a Dynamical system, background, motivating examples.
- Limit Sets and Recurrence, Van der Varden’s theorem as an application.
- Basic notions in topological dynamics: Topological transitivity, minimality, topological Mixing, Expansiveness, Equicontinuity.
- Circle rotations, homeomorphisms of the circle, rotation numbers and Denjoy’s theorem.
- Topological entropy.
- Automorphisms of the torus, automorphisms of compact groups.
- Shift spaces and shifts of finite type
- Brief introduction to ergodic theory: Equidistribution, unique ergodicity.