In this lecture we introduce and apply index theory to the study of dynamical systems. We use the vector field of the differential equation to compute a winding number, termed the index, of closed curves in the plane. We introduce the basic properties and show that through the definition we can further discuss the index of a fixed point. We put all of this together and go back to our rabbits and sheep model from Lecture 17 to show that no closed orbits can exist in that system.
This course is taught by Jason Bramburger for Concordia University.
More information on the instructor: https://hybrid.concordia.ca/jbrambur/
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