The group of invariants of an inner function with finite spectrum
This paper determines the group of continuous invariants corresponding to an inner function circle dot with finitely many singularities on the unit circle T; that is, the continuous mappings g : T -> T such that circle dot o g = circle dot on T. These mappings form a group under composition.
Journal of Mathematical Analysis and Applications
Chalendar, Isabelle; Gorkin, Pamela; and Partington, Jonathan R.. "The group of invariants of an inner function with finite spectrum." Journal of Mathematical Analysis and Applications (2012) : 1259-1267.