
Venue
Nord Pas de Calais/Belgium
Congress of Mathematics,
Université de Mons,
30 October 2013.
Abstract An endomorphism T of an object can be viewed as a discretetime dynamical system: perform one iteration of T with every tick of the clock. This dynamical viewpoint suggests questions about the longterm destiny of the points of our object. (For example, does every point eventually settle into a periodic cycle?) A fundamental concept here is the "eventual image", a companion to the algebraic concepts of image and kernel. Under suitable hypotheses, it can be defined as the intersection of the images of all the iterates T^{n} of T. I will explain its behaviour in three contexts: one settheoretic, one algebraic, and one geometric. I will also present a unifying categorical framework, showing that the eventual image has not one but two universal properties, dual to one another. In this, it resembles other important constructions such as direct sum in an abelian category. Slides In this pdf file. Related posts
