A pseudorotation with quadratic irrational rotation number

Abstract

We show, by explicit construction, that for any quadratic irrational number α \alpha , there exists a pseudorotation on an indecomposable cofrontier Λ \Lambda with α \alpha as its rotation number. Our construction builds on a family of examples of Brechner, Guay, and Mayer. They observe that in the pseudorotations they construct, irrational numbers of constant type are not realized as rotation numbers. Circle rotations can realize any rotation number, but this is to our knowledge the first example of a pseudorotation with a quadratic irrational rotation number, and hence an irrational of constant type.