We show, by explicit construction, that for any quadratic irrational number α, there exists a pseudorotation on an indecomposable cofrontier Λ with α as its rotation number. Our construction builds on a family of examples of B. L. Brechner, M. D. Guay and J. C. Mayer [in: Continuum theory and dynamical systems. Papers of the conference/workshop on continuum theory and dynamical systems held at
... [Show full abstract] Lafayette. New York: Marcel Dekker, Inc.. Lect. Notes Pure Appl. Math. 149, 59–82 (1993; Zbl 0795.58040)]. 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.