Morse theoretical methods in Hamiltonian dynamics

Hamiltonian equations describe evolution of physical systems coming for example from classical mechanics or electrodynamics. For a complicated energy function it is often very difficult to give a precise solution of a given system. One possible way to overcome this problem is to use topological methods on infinite-dimensional spaces. In this project we modify known research methods in such a way that they can be applied to the open problems, in particular, to Hamiltonian systems with a non-standard kinetic energy or Hamiltonian systems with a standard kinetic energy but with a complicated configuration space. We are concerned with topological methods such as infinite-dimensional versions of Morse homology, Floer homology, Conley index and variational methods if it is possible to define an underlying action functional.

We are working over this project in the team consisting of 5 people from the Faculty of Applied Physics and Mathematics of Gdansk University of Technology, the Polish coordinator: J. Janczewska, and 6 people from the Faculty of Mathematics of Ruhr University Bochum, the German coordinator: A. Abbondandolo. The German-Polish team received financial support from DAAD and MNiSW for two years: 2016-2017. The project supports also young researchers at the beginning of their career. Increased mobility and training are to serve first of all the integration of Polish and German young mathematicians and intensify joint research in the coming years.

 

Contact:
Ph.D., D.Sc., Assoc. Prof. Janczewska Joanna, e-mail: joanna.janczewska@pg.edu.pl, phone: +48 58 347 20 93
Prof. Ph.D., D.Sc. Izydorek Marek, e-mail: marizydo@pg.edu.pl, phone: +48 58 347 10 98