The University of Arizona

Homeomorphisms of a circle, II: Factorization

Homeomorphisms of a circle, II: Factorization

Series: Mathematical Physics and Probability Seminar
Location: Math 402
Presenter: Mark Dalthorp, University of Arizona

I will begin by recalling how we are attempting to factor a general homeomorphism of the circle as a composition of single-parameter building blocks (which are analogous to multiples of sine functions). Analogous to linear Fourier series, we want to describe how decay properties of the parameters correspond to smoothness properties of the composition. The point of the talk is present a number of theorems which describe the basic properties of this forward map, most importantly when the composition is actually invertible, hence a homeomorphism.

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