Ergodic theory and dynamical systems 1000-1S25TEUD

The theory of thermodynamic formalism, developed in the 1970s by R. Bowen, D. Ruelle, and J. Sinai, has its roots in statistical mechanics — a physical theory dealing with systems of many interacting particles and describing their behavior using methods derived from probability theory. Thermodynamic formalism has become an important tool for describing the ergodic properties of dynamical systems. It also has deep connections with dimension theory in fractal geometry.

During the seminar we will present the basic concepts and theorems of thermodynamic formalism, such as topological and theoretic entropy, symbolic dynamics, the Perron-Frobenius operator, topological pressure, Gibbs measures, the variational principle, Bowen's formula, as well as applications of the theory in holomorphic dynamics and the study of conformal iterated function systems.

In the winter semester, we will mainly discuss the material contained in the monographs listed in the course literature. In the summer semester, we will refer to research articles related to the topics discussed.