An Introduction to Rotation Theory

Prize winner, DSWeb Student Competition, 2007

By Christian Kuehn
An Introduction to Rotation Theory
This tutorial introduces one of the most fundamental dynamical systems by studying maps of the circle to itself. We are mainly going to investigate homeomorphisms of the circle. 

Homeomorphisms look easy at first sight, but this tutorial should convince you that this first impression is not quite correct. Indeed, we shall meet several surprising phenomena and discuss results, which demonstrate the complications arising already in 1-dimensional dynamics. 

Even in higher-dimensional problems it often turns out that we can reduce our system to a 1-dimensional setup, so that we are also trying to give major tools and results, which should be helpful even if you are not planning to stay in the 1-dimensional world. The theory associated with self-maps on the circle sometimes goes by the name "Rotation Theory" and as we shall see: This name is justified.
Author Institutional Affiliation
Christian Kuehn
Cornell University
Center for Applied Mathematics
Author Email
Tutorial LevelBasic Tutorial
Contest EntryYes

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