\(k\)-symplectic Lie systems: theory and applications (Q2255122)

A Lie system is a system of first-order ordinary differential equations whose general solutions can be expressed as a function, called superposition rule, of a generic finite set of particular solutions and a set of constraints. The present work is devoted to a new type of Lie systems called \(k\)-symplectic Lie systems and admitting Vessiot-Guldberg Lie algebras of Hamiltonian vector fields relative to the presymplectic forms of a \(k\)-symplectic structure. A main result is that \(k\)-symplectic Lie systems can be considered as Dirac-Lie systems in several non-equivalent ways.