Thursday, September 12, 2019

Continued Fractions and Smooth Conjugacies

David Barros

Abstract: Denjoy's Theory provides clear sufficient conditions for a topological conjugacy between a circle diffeomorphism and a rigid irrational rotation. Unfortunately, increasing f's regularity is not enough to prove any further regularity of the conjugacy map. There are indeed necessary additional hypothesis on the rotation number, regarding its approximation by rational numbers. Rotation number's continued fraction expansion turns out to be a very important tool, enabling the formulation of powerful arguments throughout the theory and the observation of beautiful interactions between analysis, number theory, and dynamical systems.

Thursday, September 12, 2019
Time: 11h30
Room: C6.2.33, Faculdade de Ciências, UL