- Teacher: Tsviqa Lakrec
Dynamical systems are a central object of study in mathematics and science. From an abstract point of view, any mapping of a space to itself can be considered as a dynamical system. Of particular importance are mappings which are either continuous or measurable. These two classes of dynamical systems are studied respectively in topological dynamics and in ergodic theory. The course will cover basic notions and results in these two areas, and their applications to various dynamical systems. Later topics will be covered depending on time restrictions.
- Measurable dynamics: measure preserving systems, ergodicity and mixing, Poincare recurrence, ergodic theorems, Hopf and ergodic decomposition, entropy.
- Topological dynamics: minimal systems, distal and proximal dynamics, topological entropy, variational principle.
- Hyperbolicity: Lyapunov exponents and Oseledets theorem.
- Dynamics of group actions.
- Measurable dynamics: measure preserving systems, ergodicity and mixing, Poincare recurrence, ergodic theorems, Hopf and ergodic decomposition, entropy.
- Topological dynamics: minimal systems, distal and proximal dynamics, topological entropy, variational principle.
- Hyperbolicity: Lyapunov exponents and Oseledets theorem.
- Dynamics of group actions.