# Cantor Minimal Dynamics

Ian F. Putnam (University of Victoria)Jan 1, 2021 — Jun 1, 2021

## About the course

The official title ‘Topology’ of this course is misleading. A better one would be ‘Topics in Dynamical Systems’. Dynamical systems is the mathematical study of models based on the idea of a topological space, representing the possible configurations of a system and a continuous map (or maps) which represent its time evolution. The systems considered in this course have two additional features: the space is compact and totally disconnected while the map is minimal in the sense that every trajectory formed by iteration on a single point is dense. Such spaces have a strongly combinatorial feel to them and one of our main goals is o provide a complete model for such systems based purely on combinatorial data called a Bratteli diagram. This model has been used extensively in topological dynamics over the last thirty years. The second main topic is to introduce a purely algebraic invariant for such systems. So the course becomes an interesting mix, moving between combinatorics, algebra and topology or dynamical systems. The overall goal is a theorem which classifies such systems up to a notion of orbit equivalence. Primarily, we will aim to understand all of the ingredients for the theorem and have some idea of how to prove it.

# Registration

This course is available for registration under the Western Dean's Agreement. To register, you must obtain the approval of the course instructor and you must complete the Western Dean's agreement form , using the details below. The completed form should be signed by your home institution department and school of graduate studies, then returned to the host institution of the course.

## Enrollment Details

- Course Name
- Topology
- Date
- Jan 1, 2021 — Jun 1, 2021
- Course Number
- MATH 540
- Section Number
- A01
- Section Code

## Instructor(s)

For help with completing the Western Dean’s agreement form, please contact the graduate student program coordinator at your institution. For more information about the agreement, please see the Western Dean's Agreement website

# Other Course Details

### Textbook

The text is the book Cantor MInimal Systems, written by the lecturer and published by the AMS:

It is my intention to cover all 14 Chapters, at least partially.

### Grading Scheme

The grading scheme for the course will be six assignments, due roughly every two weeks. They will be weighted equally and the lowest score will be dropped before computing a final grade. There will be no tests. Students will be expected to submit their own work only, but may feel free to discuss the problems with others.

### Schedule

The course will be online: lectures Monday and Thursday from 11:30 am to 12:50 pm. I intend to use the first part of each lecture as a discussion for the entire class. Depending on how long these take, it may be necessary to supplement the material with recorded (i.e. asynchronous) lectures.