Shadowing—The Anosov–Bowen approach to hyperbolicity. Lecture 1

Anosov suggested (and Katok implemented) an approach to hyperbolic dynamics in which shadowing is the central concept. For the ergodic theory of hyperbolic dynamical systems this was central to Bowen's approach. This course centers on flows and presents the scope of this approach, presenting chain decomposition, Conley Theory, spectral decomposition, structural stability, and equilibrium states. In the literature, this approach does not seem to have been implemented to this extent before.
The initial parts of the course are notionally self-contained without prerequisites, though it probably helps to have seen some dynamical systems before. When it comes to the Bowen Theory, the basic notions of ergodic theory will be assumed, up to ergodicity and mixing. I don't know yet how heavy I will get on technicalities there. The initial two lectures should be easy.
To get the link to the Zoom meeting please fill in the registration form (see URL below). In case of any troubles please contact Alexey Klimenko: klimenko@mi-ras.ru.