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

Lie systems form a special class of differential equationsadmitting many interesting geometric properties, e.g. their generalsolution can be expressed by each generic family of particular solutionsin terms of a (nonlinear) superposition rule. The main aim of this talk isto show a modern geometric approach to these systems. Such an approachhas proven to be very successful not only in describing geometricproperties of these systems but also in generalizing, in different ways,the Lie system notion.As a result, many applications of these systems have arisen in QuantumMechanics, Classical Mechanics, integrability of differential equations, Control Theory, Financial Mathematics, etc.