Lecture 15 - More Circle Maps: Toral flows, translations and circle homeomorphisms

Today, we continue with our characterization and classification of toral flows, but move into higher dimensions.  The results are pretty much the same, and again, rely on rigid rotations of each circle in the torus to characterize the flow.  But there is a twist (sorry for the pun) when we look at the time-1 map, an example of what we call a toral translation, or multi-dimensional rotation.  We will detail this today.

Next, we will go back to simple circle maps, but move into a more general area of circle homeomorphisms rather than just rigid rotations.  It turns out that even here, there is a sort of rigidity (in that not much can happen) that is somewhat surprising.  For example, is a circle map has a n-periodic point, then it can only have possibly other points of period n, and no other period is possible other than n.  We will talk about why today. 

The link is here.  See you today.

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