Dynamical Topology: Slovak Spaces and Dynamical Compactness

The area of dynamical systems where one investigates
dynamical properties that can be described in topological terms is
called "Topological Dynamics". Investigating the topological properties
of spaces and maps  that can be described in dynamical terms is in a
sense the opposite idea. This area is called "Dynamical Topology".

We will speak on two new notions: "Slovak Space" and  "Dynamical
Compactness"  for (discrete) dynamical systems given on compact metric
spaces  with continuous (surjective) self-maps.
Slovak Space is a dynamical analogue of the Rigid Space (by Johannes
de Groot and Howard Cook). Dynamical Compactness is a new concept of
chaotic dynamical systems.  In particular, we will show that all
dynamical systems are dynamically compact with respect to a
Furstenberg family  if and only if this family has the finite
intersection property.

Based on a work by Tomasz Downarowicz, Lubomir Snoha and Dariusz Tywoniuk,
and joint works with Wen Huang, Danylo Khilko, Alfred Peris, Julia Semikina and
Guo Hua Zhang.