Multicorns are not Path Connected - Archive ouverte HAL Access content directly
Book Sections Year : 2014

Multicorns are not Path Connected


The "multicorn" is the connectedness locus of unicritical antiholomorphic polynomials $z\mapsto \bar r{z}^d+c$; the special case $d=2$ was named "tricorn" by Milnor. It appears as a natural local configuration in spaces of real cubic polynomials. We prove that no multicorn for $d\ge 2$ is pathwise connected, confirming a classical prediction based on numerical observations.

Dates and versions

hal-01297669 , version 1 (04-04-2016)



John H. Hubbard, Dierk Schleicher. Multicorns are not Path Connected. Frontiers in Complex Dynamics: In Celebration of John Milnor's 80th Birthday , Princeton University Press, pp.73-102, 2014, 9780691159294. ⟨10.2307/j.ctt5vjv7b.9⟩. ⟨hal-01297669⟩
324 View
0 Download



Gmail Facebook Twitter LinkedIn More