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

Please note that the seminar will take place in room 403 in IMPAN! A Lie system is a non-autonomous system of first-order ordinary differential equations whose general solution can be expressed as an autonomous function, the superposition rule, of a generic family of particular solutions and some constants. We show that these notions are not well defined under non-autonomous changes of variables. This suggests us to define and analyse the bundle Lie systems, which are well-defined geometric notions covering Lie systems and most of their generalisations as particular cases. Reductions of Wess--Zumino--Novikov--Witten equations, multidimensional Riccati equations and other physical examples are analysed so as to illustrate our results.