A rigidity result for some parabolic germs
  The goal of this article is to prove a rigidity result for unicritical polynomials with parabolic cycles. More precisely, we show that if two unicritical polynomials have conformally conjugate parabolic germs, then the polynomials are affinely conjugate. 
Luna Lomonaco and Sabyasachi Mukherjee
math.DS math.CV