PhD theses Overview Ergodic theory is the study of statistical properties of deterministic dynamical systems. By statistical properties we mean properties which are expressed through the behaviour of time averages along trajectories of dynamical systems.
Ergodic theory overlaps with smooth dynamical systems.
Problems, examples, and methods in ergodic theory come from many branches of mathematics, including number theory, combinatorics, harmonic analysis, coding theory and group theory. I am also interested in dynamical realization of integer sequences. A rich source of examples are provided by algebraic constructions, and the structure of these systems is studied using tools from abelian harmonic analysis, commutative algebra, and finite group theory. Of particular interest are higher-order mixing and rigidity phenomena. The entropy of higher-dimensional Markov shifts is also studied.