INTRODUCTION TO ERGODIC THEORY AND DYNAMICS

Prerequisites & course information

Requisites: Graduate/professional standing Course Designation: Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: No Last Taught: Fall 2025 Learning Outcomes: 1. Analyze a range of mathematical proofs in discrete and continuous dynamical systems and recognize the underlying principles and techniques. Audience: Graduate 2. Write clear and well-reasoned mathematical arguments to describe the long time behavior of measure preserving transformations. Audience: Graduate 3. State the Birkhoff, von Neumann, and maximal ergodic theorems and reproduce their proofs. Audience: Graduate 4. Apply fundamental ergodic theorems from classical dynamics to low-dimensional examples such as the circle rotation, interval exchange transformations, and geodesic and horocycle flows on two dimensional manifolds. Audience: Graduate 5. Apply results in ergodic theory and dynamics to solve novel problems in geometric group theory and geometric topology. Audience: Graduate Learning Outcomes: 1. Analyze a range of mathematical proofs in discrete and continuous dynamical systems and recognize the underlying principles and techniques. Audience: Graduate 2. Write clear and well-reasoned mathematical arguments to describe the long time behavior of measure preserving transformations. Audience: Graduate 3. State the Birkhoff, von Neumann, and maximal ergodic theorems and reproduce their proofs. Audience: Graduate 4. Apply fundamental ergodic theorems from classical dynamics to low-dimensional examples such as the circle rotation, interval exchange transformations, and geodesic and horocycle flows on two dimensional manifolds. Audience: Graduate 5. Apply results in ergodic theory and dynamics to solve novel problems in geometric group theory and geometric topology. Audience: Graduate