Seminar za matematično fiziko

Constanza Rojas-Molina Laboratoire AGM-Analyse, G'eom'etrie et Mod'elisation Universit'e de Cergy-Pontoise, France Predavanje bo v torek 17.1.2012, ob 16:15 v predavalnici 2.03 na Jadranski 21. Petnajst minut pred predavanjem vabljeni na klepet ob čaju. Več informacij na domači strani seminarja: http://www.fmf.uni-lj.si/mafisem

Predavanje bo v torek 17.5.2011 ob 16:15 v predavalnici 2.02 na Jadranski 21. Petnajst minut pred predavanjem vabljeni na klepet ob čaju. Več informacij o seminarju: www.fmf.uni-lj.si/mafisem

Predavanje bo v torek 15.1.2011 ob 17h v predavalnici 2.03 na Jadranski 21. Petnajst minut pred predavanjem vabljeni na klepet ob čaju. Več informacij o seminarju: www.fmf.uni-lj.si/mafisem

Predavanje bo v torek 21.12.2010 ob 16:15 v predavalnici 2.03 na Jadranski 21. Petnajst minut pred predavanjem vabljeni na klepet ob čaju.

George Papamikos, Center za uporabno matematiko in teoretično fiziko, Univerza v Mariboru Some group theoretic methods for integrating differential equations due to Sophus Lie and Emmy Noether are introduced and in the end applied to a class of time-dependent nonlinear oscillators. In particular, in the first part of this talk some basic concepts will be briefly introduced; namely: continuous groups of transformations, their infinitesimal generators and their invariants. Moreover, the concept of a symmetry of a differential equation will be discussed, as well as simple methods of finding those symmetries (using Lie's algorithm) and methods of using them (reducing the order of the differential equation). In the second part, Lie's formalism will applied to Lagrangian and Hamiltonian mechanics. Two versions of the theorem of Emmy Noether will discussed and connections with constants of motions will be established. In the third part, Lie's method will be applied to a class of time-dependent, nonlinear oscillators with cubic nonlinearity. A classification of different cases with respect to their Lie point symmetries will be presented and the corresponding reductions of the order of each equation will be given. In some of these cases a second reduction, i.e. integration, is possible due to the special character of the symmetry, namely to preserve also the action integral (that is to be of Noether type). In such cases explicit exact analytic solutions of the underlying systems are given.

Predavanje bo v sredo, 23.4.2008 ob 16:15 v predavalnici 2.02 (J21). Petnajst minut pred predavanjem vabljeni na caj in piskote! Vec informacij o seminarju: www.fmf.uni-lj.si/mafisem

V sredo, 26.3.2008, 16.15 v predavalnici 2.02, FMF UL, Jadranska 21, Ljubljana.

V sredo, 12.3.2008, 16.15 v predavalnici 2.02, FMF UL, Jadranska 21, Ljubljana.

Sreda, 13.2.2008, 16:15-17:15 v predavalnici 2.02, FMF UL, Jadranska 21, Ljubljana