W środę 18.04.2012 godz. 13:15 w sali s3/11 odbędzie się referat na temat: ,,Symbolic Methods in Studying Linear Hamiltonian Systems of Differential Equations with Periodic Coefficients”. Referuje: Prof. Alexander Prokopenya. Streszczenie: We have considered two approaches used in studying linear Hamiltonian systems of differential equations. The first one is based of a classical Floquet-Liapunov theory and permits to find the principal fundamental matrix in the form of converging series in powers of a small parameter. Besides, one can construct a canonical transformation reducing the system of differential equations with periodic matrix to the system with constant matrix. The second approach is based on the infinite determinant method and permits to compute characteristic exponents of the system and to find boundaries between the domains of stability and instability in parameter space.
Both methods have been implemented in the case of the second and fourth order hamiltonian systems arising in the restricted many-body problems and the Mathematica system has been used as a tool for doing all symbolic computations.