You are currently browsing the tag archive for the ‘topological dynamics’ tag.

Before we begin or study of dynamical systems, topological dynamical systems, and measure-preserving systems (as defined in the previous lecture), it is convenient to give these three classes the structure of a category. One of the basic insights of category theory is that a mathematical objects in a given class (such as dynamical systems) are best studied not in isolation, but in relation to each other, via morphisms. Furthermore, many other basic concepts pertaining to these objects (e.g. subobjects, factors, direct sums, irreducibility, etc.) can be defined in terms of these morphisms. One advantage of taking this perspective here is that it provides a unified way of defining these concepts for the three different categories of dynamical systems, topological dynamical systems, and measure-preserving systems that we will study in this course, thus sparing us the need to give any of our definitions (except for our first one below) in triplicate.

Read the rest of this entry »

Archives

RSS Google+ feed

  • An error has occurred; the feed is probably down. Try again later.

RSS Mathematics in Australia

  • An error has occurred; the feed is probably down. Try again later.
Follow

Get every new post delivered to your Inbox.

Join 3,892 other followers