Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Dynamics, Geometry, & Groups Seminar


Friday, February 14th, 2020

Time: 10:30 a.m Place: Jeffery Hall 319

Speaker: Francesco Cellarosi (Queen's University)

Title: Denjoy's non-transitive diffeomorphisms of the circle.

Abstract: H. Poincaré proved that an orientation-preserving homeomorphism f of the circle with irrational rotation number \alpha is semi-conjugate to the rotation by \alpha. Moreover, he proved that if the homeomorphism f is transitive, then the semi-conjugacy is a homeomorphism (and hence a conjugacy) and that if f is not transitive, then the semi-conjugacy is not invertible (and hence not a conjugacy). A. Denjoy constructed examples of non-transitive homeomorphisms (in fact, diffeomorphisms) of the circle with arbitrary irrational rotation number. I will review the history of the problem and explain Denjoy's construction.