## 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.