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A classification of circle homeomorphisms

Benjamin Randeris Johannesen
(Institut for Matematik, Aarhus Universitet)
Foredrag for studerende
Fredag, 17 april, 2015, at 15:15-16:00, in Aud. D4 (1531-219)
In 1885 Henri Poincaré initiated a study of iterations of circle homeomorphisms in order to obtain qualitative information about trajectories on the torus in an attempt to classify solutions to ordinary differential equations on the torus. His results lead to a classification of circle homeomorphisms, which was developed further by Arnaud Denjoy, Michael Herman among others.  The study of circle homeomorphisms was later resumed in operator algebra by associating operator algebras to circle homeomorphisms, and the  invariant used for classifying circle homeomorphisms incidentally reappeared in the classification of  these operator algebras.

The talk will take a bottom-up approach with emphasis on classification of circle homeomorphisms.