Intersections between boundaries of bounded hyperbolic components of cubic polynomials

作者：Qiu, Weiyuan; Wang, Yueyang^*

来源：Mathematische Zeitschrift, 2023, 305(4): 55.

DOI：10.1007/s00209-023-03372-w

• Hyperbolic component
• Cubic polynomials
• Holomorphic Motion
• Periodic slices

We are concerned with the intersections between the boundaries of bounded hyperbolic components in the space of cubic polynomials. We show that if the intersection map has an attracting periodic orbit, then it is either a parabolic map or a Misiurewicz map. This result is based on a complete classification of all these intersection maps in one-dimensional slices S-p introduced by J. Milnor, which consists of cubic polynomials with a periodic p critical point.

• 单位
  复旦大学