Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

In my talk, I will present the energy-momentum method, which allows for studying stability and bifurcation of Hamiltonian systems with symmetry. First I will introduce a symplectic action of Lie groups and momentum map. After this introduction, I will discuss the symplectic structure on reduced space (quotient space) and explain the conditions on the stability of these systems. In the last part, I will present the energy-momentum method and briefly describe how it can be applied.