Multicorns are not path connected

  title={Multicorns are not path connected},
  author={John H. Hubbard and Dierk Schleicher},
The tricorn is the connectedness locus in the space of antiholomorphic quadratic polynomials z 7! z2 + c. We prove that the tricorn is not locally connected and not even pathwise connected, confirming an observation of John Milnor from 1992. We extend this discussion more generally for antiholomorphic unicritical polynomials of degrees d 2 and their connectedness loci, known as multicorns. 


Publications citing this paper.


Publications referenced by this paper.
Showing 1-10 of 14 references

Dynamics in one complex variable, 3rd edition

  • John Milnor
  • Annals of Mathematics Studies
  • 2006

A parabolic Pommerenke-Levin-Yoccoz inequality

  • BE Xavier Buff, Adam Epstein
  • Fund. Math. 172
  • 2002

SCHLEICHER [ BE ] Xavier Buff and Adam Epstein , A parabolic PommerenkeLevinYoccoz inequal

  • D.
  • 2002

Bifurcation of parabolic fixed points

  • Mitsuhiro Shishikura
  • The Mandelbrot set, theme and variations,
  • 2000

Connectedness of the Tricorn

  • Na Shizuo Nakane
  • Ergod. Th. & Dynam. Sys
  • 1993

Similar Papers

Loading similar papers…