Topological methods in modelling the dynamics of natural phenomena

Topological methods based on topological invariants such as fixed point index or Lefschetz number are useful instruments in studying dynamical systems, which model physical and biological phenomena. They allow one to obtain a range of valuable information about the system, related for example to existence of fixed or periodic points, their amount andlocation. It is of great importance from the point of view of the modeled phenomena, in which it is important to detect the periodic occurrence of certain basic values.

The project has interdisciplinary character because special attention will be focused on low-dimensional and smooth systems, which model real physical and biological processes.