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.

Introduction to topological dynamics

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