Prof. James Muldowney
University of Alberta，Canada
The evolution in dynamical systems of differential k-forms has proved to be a versatile tool. It facilitates the investigation of local and global properties as well as steady state behaviour; topics such as existence and stability of periodic orbits and questions of dimension of invariant sets especially global attractors. The main tools in finite dimensional dynamics have been multiplicative and additive k-compound matrices whose algebraic, metric and spectral properties have provided useful insights. These allow us to elicit much new information from linearized systems through associated compound differential equations. The first lecture will discuss the finite dimensional theory and applications including a higher dimensional generalization of the Bendixson-Dulac condition for the non-existence of periodic orbits.