In the local dynamics of Newton's method of a holomorphic function of two variables, a multiple root of rank 1 has a Cantor family of holomorphic superstable manifolds which consists of quadratically convergent initial values.
Yoshikazu YAMAGISHI. "On the local convergence of Newton's method to a multiple root." J. Math. Soc. Japan 55 (4) 897 - 908, October, 2003. https://doi.org/10.2969/jmsj/1191418754