The group of invariants of an inner function with finite spectrum
  This paper determines the group of continuous invariants corresponding to an inner function $ \Theta $ with finitely many singularities on the unit circle $T$; that is, the continuous mappings $g: T \to T$ such that $\Theta \circ g = \Theta $ on $\T$. These mappings form a group under composition. 
Isabelle Chalendar, Pamela Gorkin and Jonathan R. Partington
math.CV