On the invariant distributions of C^2 circle diffeomorphisms of   irrational rotation number
  We show that no C^2 circle diffeomorphism of irrational rotation number has invariant 1-distributions other than (scalar multiples of) the invariant measure. We also show that this is false in the C^1 context by giving both minimal and non-minimal examples. 
Andr\'es Navas, Michele Triestino
math.DS