Instructor: Prof. Mario Roy
Email: mroy@glendon.yorku.ca

Course Dates: January 10th - April 6th, 2023
Mid-Semester Break: February 20th - 24th, 2023
Lecture Times: Tuesdays & Thursdays | 1:00 - 2:30 PM (ET)
Office Hours: Wednesdays | 1:00 - 3:00 PM (ET)

Registration Fee: PSU Students - Free | Other Students - CAD$500

Prerequisites: Knowledge of topology and measure theory. (Though not required, knowledge of the basic theory of dynamical systems and ergodic theory is an asset.)

Evaluation: 5 assignments worth 20% each.

Capacity Limit: 35 students

Format: Online

Course Description

In this course, we examine a powerful method for constructing and studying the geometric and dynamical properties of fractal sets. It is well-known that many sets, including the middle-third Cantor set, the set of irrational numbers in $[0,1]$, and $[0,1]$ itself, can be viewed as limit sets of iterated function systems (IFSs). However, the unit circle $S^{1}$ $\subseteq$ $R^{2}$ is not the limit set of any IFS; it is, nevertheless, the limit set of a CGDMS. A CGDMS is a generalization of an IFS, with a graph comprising vertices and edges and with an edge-transition matrix. To study CGDMSs, we first need to study thermodynamic formalism of countable-state subshifts of finite type. The course will introduce the basics of dynamical systems theory, ergodic theory, fractal geometry and thermodynamic formalism.