Brigita Fercec, Center for Applied Mathematics and Theoretical Physics, University of Maribor |

Title: Integrability in planar polynomial systems of ODE’s |

Abstract: The integrability problem consists in the determination of local or global first integrals and is one of the main open problems in the qualitative theory of differential systems. An essential part of the theory of integrability of ODE’s is devoted to studying local integrability of two dimensional analytic systems of differential equations (two dimensional analytic vector fields) in a neighborhood of a singular point of center or focus type. In this talk we describe an approach for studying integrability in two dimensional polynomial systems. Then, we discuss new criteria for existence of a first integral of the certain form. |